RATE ( SPEED , DISTANCE AND TIME, WORK PROBLEM, AND WORK-RATE PROBLEM)
Summary
TLDRThis video covers essential concepts of calculating speed, distance, and time, along with average speed, through practical examples. It explains how to compute average speed for different time intervals and speeds, and applies this to real-life situations like vehicle travel and running. The video also delves into solving work-rate problems, demonstrating how to calculate how long multiple people take to complete tasks together. Using formulas for speed, distance, time, work, and rate, the video provides step-by-step solutions to problems, making the concepts easier to grasp.
Takeaways
- 📏 Distance, speed, and time are interconnected through formulas.
- 🚌 To find speed, use the formula: speed = distance / time. For example, a bus traveling 200 km in 4 hours has a speed of 50 km/h.
- 🏍️ To find the average speed of a vehicle over different time periods, first calculate the distance for each period, then find the total distance and divide by the total time.
- 🏎️ For a motorcycle traveling 36 km in 3 hours and 40 km in 2 hours, the average speed is calculated by adding both distances and dividing by the total time: 188 km / 5 hours = 37.6 km/h.
- 🏃 To find the average speed of a runner who changes speeds, calculate the distance covered at each speed and then the total distance divided by the total time.
- 🔨 Work problems can be solved using the formula: work = rate x time. The rate is often given as 1/time.
- 👷 For work problems involving two people, calculate the individual work rates and then the combined work rate.
- 🧮 To find the time remaining to complete a task when one person starts and another finishes, use the formula: time remaining = 1 - work done.
- 🧹 When solving how long it takes for two people to complete a task together, add their rates and find the combined rate.
- 📊 Use calculators for precise calculations when dealing with fractions and rates to ensure accuracy.
Q & A
What is the formula for calculating speed?
-The formula for calculating speed is: Speed = Distance ÷ Time.
In the example of a bus traveling 200 km in 4 hours, what is its speed?
-Using the formula Speed = Distance ÷ Time, the bus's speed is 200 km ÷ 4 hours = 50 km per hour.
How do you calculate the average speed when there are two different rates for a trip?
-To calculate average speed, first find the total distance by adding the distances traveled at each rate, then divide by the total time. The formula is: Average Speed = (Distance 1 + Distance 2) ÷ (Time 1 + Time 2).
In the motorcycle problem, how do you find the total distance and total time?
-For the motorcycle problem, first find the distance for each rate: 36 km/h for 3 hours gives 108 km, and 40 km/h for 2 hours gives 80 km. The total distance is 108 km + 80 km = 188 km, and the total time is 3 hours + 2 hours = 5 hours.
What is the motorcycle's average speed over the two time periods?
-The average speed is calculated by dividing the total distance by the total time: 188 km ÷ 5 hours = 37.6 km per hour.
In the problem where Katy runs at two different speeds, how is the average speed calculated?
-First, calculate the distance for each speed: 15 km/h for 2 hours gives 30 km, and 8 km/h for 1 hour gives 8 km. The total distance is 38 km, and the total time is 3 hours. The average speed is 38 km ÷ 3 hours = 12.6 km per hour.
What is the formula for calculating work when rate and time are given?
-The formula for work is: Work = Rate × Time.
In the chair-assembling problem, how long did it take Look to finish assembling the chair after Phil worked on it for 20 minutes?
-Phil worked for 20 minutes, completing 2/3 of the work. The remaining work was 1/3. Look took 20 minutes to complete the remaining 1/3 of the work.
How do you calculate the time remaining to complete a task if part of it has been completed?
-The time remaining is calculated by the formula: Time Remaining = 1 - Work Done.
How long did it take Alex to finish cleaning the room after Haley cleaned for 1 hour?
-Haley worked for 1 hour, completing 1/2 of the work. The remaining 1/2 of the work took Alex 1.5 hours to complete.
Outlines
🚍 Calculating Speed and Average Rate in Motion Problems
This paragraph discusses how to calculate speed using the formula speed = distance ÷ time. A problem is solved where a bus travels 200 kilometers in 4 hours, resulting in a speed of 50 km/h. Another example follows where the average speed of a motorcycle is computed. The motorcycle covers 36 km in 3 hours and 40 km in 2 hours. The process involves calculating the total distance (108 km + 80 km = 188 km) and dividing by the total time (5 hours) to find the average speed, which is 37.6 km/h.
🪑 Work Rate Problems: Chair Assembly Example
This paragraph focuses on work rate problems, using the formula Work = Rate × Time. A scenario is provided where Phil assembles a chair in 30 minutes and his son takes 60 minutes. Phil works for 20 minutes, and the problem is to determine how long his son will take to finish the task. Using work rate formulas, it is determined that Phil completes 2/3 of the task, leaving 1/3 for his son. His son, with a rate of 1/60 chairs per minute, finishes the remaining work in 20 minutes.
🧹 Cleaning the Room: A Shared Task Problem
This paragraph describes a shared work problem where Haley and Alex clean a room. Haley can clean the room in 2 hours, and Alex in 3 hours. Haley works for 1 hour, and the task is to find how long Alex will take to finish the job. After calculating the work done by Haley (1/2), the time remaining is found to be 1/2. Alex’s rate is 1/3 rooms per hour, so the time required for Alex to finish the job is calculated as 1.5 hours.
🏠 House Painting: Joint Effort Problem
This paragraph explains a scenario where Betty and Jan are painting a house together. Betty can paint the house in 6 days, and Jan can paint it in 8 days. The problem is to calculate how long it will take them to paint the house if they work together. Using the formula for combined rates, 1/6 + 1/8, the total rate is found to be 7/24 houses per day. The time required to paint the house is then calculated as 3.42 days.
Mindmap
Keywords
💡Speed
💡Distance
💡Time
💡Average Speed
💡Work
💡Rate
💡Distance-Time Relationship
💡Task Sharing
💡Fractional Time
💡Problem Solving
Highlights
Introduction to distance, speed, and time formulas with a bus travel example.
Speed formula: speed equals distance divided by time. Example: 200 km in 4 hours equals 50 km/h.
Average speed calculation using multiple speeds for different time periods. Example of a motorcycle traveling 36 km for 3 hours and 40 km for 2 hours.
Step-by-step breakdown of finding distance for two different speeds: 108 km for 36 km/h over 3 hours and 80 km for 40 km/h over 2 hours.
Calculating average speed by summing the distances (108 km + 80 km = 188 km) and dividing by total time (5 hours), yielding an average speed of 37.6 km/h.
Another average speed example with a runner: 15 km/h for 2 hours and 8 km/h for 1 hour, resulting in an average speed of 12.6 km/h.
Introduction to work rate problems and formulas, including work equals rate times time.
Rate formula: rate equals 1 divided by time. Demonstrating with Phil and his son assembling a chair.
Phil works for 20 minutes assembling the chair, completing 2/3 of the task.
Using time remaining formula: time remaining equals 1 minus the completed work, resulting in 1/3 of the work left.
Calculating the son's work rate, where the remaining work takes him 20 minutes to finish assembling the chair.
Work rate problem example with Haley and Alex cleaning a room together, calculating how long Alex needs to finish the task after Haley starts.
Introduction to another work rate problem: Betty and Jan painting a house together.
Calculating the combined work rate of two workers using the formula 1/A + 1/B, demonstrating with Betty and Jan's task.
Final example results in Betty and Jan finishing the painting task in 3.42 days.
Transcripts
rate of objects and rational
numbers so first is we going to discuss
distance speed and time so these are the
formula for this distance speed and
time so for example here we have a
problem a bus travel 200 kilm in 4 hours
what is its
speed so using the speed formula we have
speed is equals to distance divide time
and speed is equals to your distance is
200 kilm in time is 4 hours so speed is
equals to 50 kilm per hour so that's how
you compute the
speed uh distance and time you use the
formula
so okay so we have here another problem
a BMW gs1 1260 can travel at a rate of
36 kilm for 3 hours and 40 km for the
next 2 hours what is the average rate of
the
motorcycle so the question here is what
is the average rate so we have the First
Rate which is 36 kilm for 3 hours and
the next rate which is 40 kilm for the
next 2
hours so to solve this one we begin with
step one Sol for 36 kilm uh for per 3
hours 36 kilm per hour for 3 hours so
this problem need uh uh needs to find
the distance so the distance is equals
to speed time time the distance is
equals to 36 km/ hour * 3 and the answer
is 108
kilm okay next is for the step two solve
for 40 km/ hour for the next 2
hours so we have here the distance is
equals speed time time and the distance
is equals to 40
kilm per hour time 2 hours and 40 * 2
that is 80 okay for step three okay we
need to find the uh average okay so
solve for the average rate so we have
here so da stands for distance average
is equal to distance 1 plus distance 2
ta n is equals to our time average is
equals to T1 + T2 and we have the speed
is equals to distance uh average divide
time
average so D1 class is step one distance
and step two is the D2 okay so we have
108 km plus 80 km
so the distance average is equals to
188
kilm okay so that's the da now solving
for ta okay ta Nam is the RS RS step one
RS n step two so Step One is 2 hours
while step two is 3 hours so that is T1
and
T2 so ta is equals to 5 hours now
solving for the speed so this last uh
column here is the speed so distance
average divide time average and that is
188 kilm y then 5 hours that is iton so
the speed is equals to 37.6 km per
hour okay next problem so we have
another problem which is the same
um Kina Katy runs at a rate of 15 kilm
per hour for two hours after that she
slow down to 8 kilm for the next hour
what is her average
speed so to compute for the speed
first step one step
one 15 km per hour for 2 hours so that
is distance that is 30 and the distance
next problem which is 8 km per hour for
the next hour next hour is 1 hour okay
equivalent to 1 hour so the distance is
equals to 8 kilm now solving for the
average rate or your speed we have da is
equal to
38 and ta is equal to 3 hours Sil okay
we have da a TA then we have the speed
okay 38 km divide 3 hours that is 12.6
km per hour okay the answer is 12.6 km
per
hour okay for the next topic we have
word problem a work problem so we have
here formula tatong formula to remember
work is equals to rate time time and the
rate this rate s formula rate is
equivalent to one over time okay we'll
discuss it later
to further understand and the last time
and the last formula is work time is
equals to time remaining divide rate
okay let's use this to an actual
problem okay fi okay field can assemble
a chair in 30 minutes his sonl can
assemble the chair in 60 minutes Bill
work on the task for 20 minutes and let
his son work on the rest how long will
it take look to finish assembling the
chair so so we have here a problem no so
the question here is how long will it
take look to finish assembling the chair
so let's go on with the solution so step
one so we have here the given so
remember that phield can assemble a
chair in 30 minute so in 30 minutes no
all individual so this is the individual
rate okay so field only field can finish
assembling a chair in 30 minute so the
rate the rate here means the individual
rate
Kip look okay so we have here uh rate
equals to one over time and the time
used in rate is rate time individual so
K is 30 30 so we have rate is equals to
1 over 30 okay so now we have to find
the work okay work is equals to rate
time time so the work here is equals to
1 over 30 rate while the time is used
for okay work is to
solve remember Phil okay Phil and uh his
sonl work together to finish the same
task okay
yeah okay so fi work on the task for 20
minutes so we have the time is 20 so
multiply L uh 1 / 30 * 20 you can use a
calculator
here okay 1
over3 divide 20 and the answer is and
multiply
Pala the answer is 2/3 so the answer is
2/3 okay next step
two note we have a note here formula for
time remaining is 1 minus work so this
is a constant
formula so always remember this formula
for the time
remaining so to solve for the time
remaining time remaining equals 1us 2/3
remember the 2/3 is work work
so we have 1 - 2/3 okay we use the
calculator okay
1 1
-
2/3 will equals to 1/3 so the time
remaining is
1/3 okay now solving for work time of
look so remember that that the work time
is equals to time remaining divide rate
and time remaining is equals to
1/3 okay so individual Work N okay so
individual remember that field can
finish in 30
minutes while look can finish in 60
minutes okay so look can assemble the
same chair in 60 minutes so the rate of
look is 1 / 60 remember 1/ 60 is the
rate
of minutes
so we have here work time is equals to
remember the time remaining is 1/3
divides 1 / 60 which is the rate of look
so to calculate in
calculator 1/
3
divides 1 /
60 the answer is 20 so we have here the
work time for look is 20
minutes this means that Phil finish the
work for 20 minutes and then look also
finish it within 20
minutes okay for another problem the
same problem Hy and Alex are sharing a
room Haley can clean their room in two
hours while Alex can clean it in 3 hours
haly cleaned the room for 1 hour and
Alex continued the rest how long did it
take Alex to clean the room so
individual rate n is for Alex Haley
first is 2 hours K Alexan is 3 hours now
uh what did what they do is they
combined their work and heey started for
1 hour and Alex continued the rest so
how long did Alex finish the
job so again solve for the rate so given
Haley can clean the room in 2 hours so
the rate of Haley is 1/2 now for the
time is 1 since Haley finished the room
uh cleaning the room in 1 hour so work
is equals 1 12 * 1 and that is equals to
1
12 okay we're going to use the
calculator the answer is
1/2 okay next solve for the time
remaining okay remember the time
remaining is one minus work again the
work okay you work Haley okay so 1 - 12
in
calculator and the answer is 1 12 so
this is the time remaining now solving
for the work time of Alex so again we
have the formula for work time work time
is equals to time remaining divide rate
and this is the time remaining and Alex
now can clean it in 3 hours so the rate
of Alex is 1/3 so work time is equals to
12 IDE 1/3 use the calculator to solve
for the work
time we have 1/2 divides 1/3 and it will
equal to 3 over two or 1 or 1/2 or 1.5
so always the answer is in a decimal or
whole number which is and the answer
here is 1.5 hours so this means that
Alex took 1.5 hours that Hal finish in 1
hour so start Alex one hour I mean Haley
then Alex into uh 1.5
hours so last for the rate is work rate
problem so this is very
easy so we have an example Betty can
paint a house in 6 days and JN can paint
the same house in 8 days how long will
it take them to paint the house so this
time both uh both
the uh both the given or Betty and Jan
okay P work time n or job n in just um
just a one scenario
okay okay one at um one time P talaga so
how do you solve this one so solving
for okay 1 a + 1 B so Betty can paint a
house in six days while Jan can paint
the same house in 8 days so B Betty is a
so
first a
Anda B so we have one six and 1 over8
y six J or a is days nil or whatever the
number it is hours maybe days maybe time
or weeks okay yeah so we have here six
and 8 so let's add it 16 +
18 1 / 6
+ 1 over 8 equals to 7
over 24
now step two solving for one / t Okay
the one over T here class
is the total of 1 a + 1 B which is 1 6
+8 = to 7 / 24 and our T is equals to
7/ 24 so in
fraction okay in
fraction one okay and time remaining mag
another fraction click Naman 7 over
24 and click the equals click the SD and
the answer is
3.42 so we're going to get the two
decimal places so the answer is 3.42
days okay so s Hindi Cas okay use this
away 1
divide okay 7 divide
24 and the answer is
3.42 okay still the same so use this one
use
parenthesis so this
is okay this is the calculator technique
okay so 24/ 7 or 3 + okay this uh this
one is an example of a mixed number so
this one three and 3 over 7 so 3
+ 3/
7al equal
to okay
3.24 okay so that is all for rate
problem
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