Question 67457: A sprinter runs the 100-meter dash, with the wind behind him, in 9.96 seconds. He then runs the same distance in the other direction in 11.79 seconds. About how fast is the wind blowing? About how fast does the sprinter run when there is no wind?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A sprinter runs the 100-meter dash, with the wind behind him, in 9.96 seconds. He then runs the same distance in the other direction in 11.79 seconds. About how fast is the wind blowing? About how fast does the sprinter run when there is no wind?
:
Let x = his speed (meters/sec) with no wind
Let y = the wind speed also in meters/sec
"
Speed with the wind = (x+y)
Speed against the wind = (x-y)
:
Write a system of distance equations: Distance = Time * Speed
9.96(x+y) = 100
11.79(x-y) = 100
:
Divide the 1st equation by 9.96 and the 2nd equation by 11.79, results:
x + y = 10.04
x - y = 8.48
---------------adding eliminates y
2x + 0 = 18.52
x = 18.52/2
x = 9.26 meters/sec with no wind
:
Find the wind using x + y = 10.04
9.26 + y = 10.04
y = 10.04 - 9.26
y = .78 meters/sec is the speed of the wind
:
Check using 11.79(x - y) = 100
11.79(9.26 - .78) =
11.79(8.48) = 99.9792 ~ 100
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