# Distance, Rate and Time

Video Solutions to help Grade 6 students learn how to use the formula distance = rate • time.

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### New York State Common Core Math Grade 6, Module 1, Lesson 22

Lesson 22 Student Outcomes

• Students decontextualize a given speed situation, representing symbolically the quantities involved with the formula distance = rate • time.

Lesson 22 Summary

Distance, rate, and time are related by the formula distance = rate • time.
Knowing any two of the values allows the calculation of the third.

Vocabulary

If something is moving at a constant rate of speed for a certain amount of time, it is possible to find how far it went by multiplying those two values. In mathematical language, we say Distance = Rate • Time

Lesson 22 Classwork

Opening Exercise
• How many seconds are in minute?
• Can you verbalize this relationship?
• Represent the relationship in two ways.

Exercise 1
Walker: Substitute the walkers' distance and time into the equation and solve for the rate of speed.
Distance = Rate • Time

Hint: Consider the units that you want to end up with... If you want to end up with the rate ( ) then divide the distance (feet) by time (seconds).

Runner: Substitute the runner’s time and distance into the equation to find their rate of speed.
Distance = Rate • Time

Exercise 2
Part 1: Chris Johnson ran the 40 yard dash in 4.24 seconds. What is the rate of speed? Round any answer to the nearest hundredth of a second.
Distance = Rate • Time

Part 2: In Lesson 21, we converted units of measure using unit rates. If the runner could keep up this speed at a constant rate, how many yards would he run in an hour? This problem can be solved by breaking it down into two steps. Work with a partner, and make a record of your calculations.
a. How many yards would he run in one minute?
b. How many yards would he run in one hour?

• We completed that problem in two separate steps, but it is possible to complete this same problem in one step. We can multiply the yards per second by the seconds per minute, then by the minutes per hour.
Cross out any units that are in both the numerator and denominator in the expression because these cancel out each other.

Part 3: How many miles did the runner travel in that hour? Round your response to the nearest tenth.

Example 1
I drove my car on cruise control at 65 miles per hour for 3 hours without stopping. How far did I go?
d = r • t

Example 2
On the road trip, the speed limit changed to miles per hour in a construction zone. Traffic moved along at a constant rate (50 mph), and it took me minutes (0.25 hours) to get through the zone. What was the distance of the construction zone? (Round your response to the nearest hundredth of a mile).

Lesson 22 Problem Set

1. If Adam’s plane traveled at a constant speed of 375 miles per hour for six hours, how far did the plane travel?

2. A Salt March Harvest Mouse ran a 360 centimeter straight course race in 9 seconds. How fast did it run?

3. Another Salt Marsh Harvest Mouse took 7 seconds to run a 350 centimeter race. How fast did it run?

4. A slow boat to China travels at a constant speed of 17.25 miles per hour for hours. How far was the voyage?

5. The Sopwith Camel was a British, First World War, single-seat, biplane fighter introduced on the Western Front in 1917. Traveling at its top speed of 110 mph in one direction for 2 1/2 hours how far did the plane travel?

6. A world class marathon runner can finish 26.2 miles in 2 hours. What is the rate of speed for the runner?

7. Banana slugs can move at 17 cm per minute. If a banana slug travels for 5 hours, how far will it travel?

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