Question 272228: Two runners start from the same point at the same time. They will be 4 miles apart at the end of two hours if running in the same direction, and they will be 16 miles apart at the end of one hour if running in opposite directions. Find their speeds.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Two runners start from the same point at the same time.
They will be 4 miles apart at the end of two hours if running in the same direction,
and they will be 16 miles apart at the end of one hour if running in opposite directions.
Find their speeds.
:
Let x = speed of the faster runner
Let y = speed of the slower
:
Write a distance equation for each scenario
:
2(x - y) = 4; running the same direction
simplify, divide by 2
x - y = 2
and
1(x + y) = 16; running opposite directions
:
Add the two equations
x - y = 2
x + y = 16
-------------addition eliminates y, find x
2x = 18
x = 9 mph is the faster runner
then
9 + y = 16
y = 16 - 9
y = 7 mph is the slower runner
:
:
Check solution in the two equations
2(9 - 7) = 4
and
1(9 + 6) = 16
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