rate distance and time

Question

A child is running on a moving sidewalk in an airport. When he runs against the sidewalk's motion, he travels
66ft
in
11
seconds. When he runs with the sidewalk's motion, he travels
88ft
in the same amount of time. What is the rate of the child on a still sidewalk and what is the rate of the moving sidewalk?

Answer 1

r represents child's rate

w represents walkway's speed

 

66 = (r - w)11

88 = (r + w)11

 

66 = 11r - 11w

88 = 11r + 11w

 

Can you solve the system?

Answer 2

Hi Ayline, let x represent the speed of the moving sidewalk. Ley y equal the speed of the child on the sidewalk.

 

Using the D(istance) = R(ate) * T(ime) equation, we can solve this problem.

 

Child moving against the sidewalk:

D = R * T

 

D = 66 feet

 

R = x - y

 

T = 11 seconds

 

Substitute:

 

66 = (x - y) * 11

 

Divide both sides by 11:

 

x - y = 6

 

Child moving with the sidewalk:

 

D = R * T

 

D = 88 feet

 

R = x + y

 

T = 11 seconds

 

Substitute:

 

88 = (x + y) = 11

 

Divide both sides by 11:

 

x + y = 11

 

We now have to equation in two unknowns:

 

x + y = 8

x -  y = 6

-------------

 

2x = 14

 

Divide both sides by 2:

 

x = 7

 

The moving sidewalk is traveling at 7 feet per second.

 

Using x + y = 8, we can solve for y:

 

7 + y = 8

 

Subtract 7 from both sides:

 

y = 1

 

The child is traveling at 1 foot per second.

 

Questions?