RATE ( SPEED , DISTANCE AND TIME, WORK PROBLEM, AND WORK-RATE PROBLEM)

Summary

This 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.