question in description

Question

A child is running on a moving sidewalk in an airport. When she runs against the sidewalk's motion, she travels
30ft
in
10
seconds. When she runs with the sidewalk's motion, she travels
72ft
in
8
seconds. What is the rate of the child on a still sidewalk and what is the rate of the moving sidewalk

Answer 1

Hi,

 

We have two situations: one where she is walking with the moving sidewalk and one where she is walking against the moving sidewalk. Let's say c is her speed and s is the sidewalk's.

 

c - s = (30 ft / 10 sec)

 

c + s = (72 ft / 8 sec)

 

We can use the process of elimination to first find c and then plug it back into one of our equations to get s.

 

c - s = 3

c + s = 9

 

2c = 12 → c = 6 ft / sec

 

c - s = 3

 

6 - s = 3 → s = 3 ft / sec

 

If you haven't learned elimination, you can substitute the equations into one another.

 

Hope this helps!

Answer 2

s represents the speed of the sidewalk

c represents the speed of the child

 

30 = (c - s)10

72 = (c + s)8

 

Can you solve the system?