﻿ Distance Rate Time Worksheet | Problems & Solutions # Distance Rate Time Worksheet

Distance Rate Time Worksheet
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1.
Jasmine walks from her home to school and back home. Her sister Susan walks from school to their home and back to school. They both walk with the constant speeds. They start exactly at the same time and meet for the first time, 7 km from school. Each one continues on the way to their destination when they both turn around without any loss of time. They meet for the second time, 4 km from their home. What is the distance from their home to school? a. 15 km b. 17 km c. 11 km d. 14 km

#### Solution:

Let 'x' be the distance from home to school

The time taken by Susan to walk 7 km is equal to the time taken by the Jasmine to walk (x - 7) km.

During the time taken by Susan to walk 1km, Jasmine walks (x - 7)7 km

Similarly, In the time Susan walks (x + 4) km, Jasmine walks 2x - 4 km.
[After completion of one round.]

If Susan walks (x + 4) km, Jasmine walks (x-7)(x+4)7 km which must be equal to 2x - 4 km.
[From steps 3 and 4.]

Solving the equation (x-7)(x+4)7 = 2x - 4
[From step 5.]

(x-7) (x+4) = 7(2x - 4)
[Multiply by 7 on both sides.]

x2 - 3x - 28 = 14x - 28
[Multiply.]

x2 - 3x = 14x
[Add 28 on both sides and simplify.]

x2 - 3x + 3x = 14x + 3x
[Add 3x on both sides and simplify.]

x2 = 17x
[Divide by x on both sides.]

x = 17 km
[Simplify.]

2.
Nine woodchucks can chuck eight pieces of wood in three hours. How much wood can a woodchuck chuck in one hour? a. $\frac{8}{27}$ b. $\frac{8}{9}$ c. $\frac{9}{8}$ d. $\frac{8}{18}$

#### Solution:

Given, 9 woodchucks can chuck 8 pieces of wood in 3 hours.

Then one woodchuck can chuck 8 / 9 of a piece of wood in 3 hours.

One woodchuck can chuck 8 / 9×3 of a piece of wood in one hour.

Therefore, one woodchuck can chuck 8 / 27of a piece of wood in one hour.

3.
The total number of birds migrated from the far south of South America to northern wintering grounds in 4 hours is 1200. Find the total number of birds migrated in 9 hours, if the rate of migration remains the same. a. 2700 b. 2121 c. 2221 d. 2200

#### Solution:

The total number of birds migrated in 4 hours = 1200

The total number of birds migrated in one hour = 1200 ÷ 4 = 300

The total number of birds migrated in 9 hours = The total number of birds migrated in one hour × number of hours

= 300 × 9 = 2700

So, the total number of birds migrated in 9 hours is 2700.

4.
840 food packets are dropped for every 3 hours in a flood affected area. Find the total number of food packets dropped in 15 hours, if the rate of dropping remains the same. a. 4600 b. 4200 c. 4621 d. 4521

#### Solution:

The total number of food packets dropped in 3 hours = 840

The total number of food packets dropped in one hour = 840 ÷ 3 = 280

The total number of food packets dropped in 15 hours = The total number of food packets dropped in one hour × number of hours

= 280 × 15 = 4200

So, the total number of food packets dropped in 15 hours is 4200.

5.
The birth rate of a whale at a coast is 140 births every 5 days. Find the number of births in 12 days, if the birth rate remains the same. a. 330 b. 1680 c. 336 d. 280

#### Solution:

The number of whale births in 5 days = 140

The number of whale births in one day = 140 ÷ 5 = 28

The number of whale births in 12 days = The number of whale births in one day × number of days

= 28 × 12 = 336

So, the number of whale births in 12 days is 336.

6.
A printing machine produces 2400 newspapers in 3 hours. At this rate, how many newspapers are produced in 14 hours? a. 24,000 b. 4800 c. 8000 d. 11,200

#### Solution:

The number of news papers produced in 3 hours = 2400

The number of news papers produced in one hour = 2400 ÷ 3 = 800

The total number of news papers produced in 14 hours = The total number of news papers produced in one hour × number of hours

= 800 × 14 = 11200

So, the total number of news papers produced by the printing machine in 14 hours is 11,200.

7.
Chicago bulls scored 1080 points in 12 matches of NBA. At this rate, how many points do you think the team would have scored in 5 matches? a. 420 b. 400 c. 450 d. 430

#### Solution:

The number of points the team scored in 12 matches = 1080

The number of points the team scored in one match = 1080 ÷ 12 = 90

The number of points the team scored in 5 matches = The number of points the team scored in one match × number of matches

= 90 × 5 = 450

So, the number of points the team scored in 5 matches is 450.

8.
The total number of births in the United States in 3 hours was 900. Find the total number of births in 7 hours if the birth rate remains the same. a. 2,100 b. 2,121 c. 2,200 d. 2,221

9.
600 cars pass the toll gate every 2 hours. Find the total number of cars passing the toll gate in 5 hours if the rate remains the same. a. 1,600 b. 1,521 c. 1,500 d. 1,621 a. 2,821 b. 2,721 c. 2,700 d. 2,800