Question 80004: please help,
A child in an airport is able to cover 372 meters in 4 minutes running at a steady speed down a moving sidewalk in the direction of the sidewalk's motion. Running at the same speed in the direction opposite to the sidewalk's movement, the child is able to cover 165 meters in 3 minutes. What is the child's running speed on a still sidewalk, and what is the speed of the moving sidewalk?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A child in an airport is able to cover 372 meters in 4 minutes running at a steady speed down a moving sidewalk in the direction of the sidewalk's motion. Running at the same speed in the direction opposite to the sidewalk's movement, the child is able to cover 165 meters in 3 minutes. What is the child's running speed on a still sidewalk, and what is the speed of the moving sidewalk?
:
Let x = speed on a still sidewalk (meters/min)
Let y = speed of the moving walkway
:
Speed With the moving walkway = (x+y)
Speed Against the moving walkway = (x-y)
:
Write two distance equations; distance = time * speed
:
4(x + y) = 372 >> 4x + 4y = 372
3(x - y) = 165 >> 3x - 3y = 165
:
Multiply the 1st equation by 3 and the 2nd equation by 4
12x + 12y = 1116
12x - 12y = 660
------------------adding eliminates y
24x + 0y = 1776
x = 1776/24
x = 74 meters/min, speed on a still sidewalk
:
Find the speed of the walkway using 4x + 4y = 372
4(74) + 4y = 372
296 + 4y = 372
4y = 372 - 296
y = 76/4
y = 19 meters/min; speed of the moving walkway
:
Check solutions using 3x - 3y = 165:
3(74) - 3(19) =
222 - 57 = 165
|
|
|
