SOLUTION: Two women live on the same street, but live 1.5 miles apart. Each morning both women begin running at the same time in the same direction. Because of where she lives, Jane is alway

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Question 581972: Two women live on the same street, but live 1.5 miles apart. Each morning both women begin running at the same time in the same direction. Because of where she lives, Jane is always 1.5 miles ahead of Sue when they start running. Jane runs at a rate of 6 mph and Sue runs at a rate of 8 mph. How far from SUE'S house are they when Sue catches up? Be sure to label your answer. Round to the nearest whole number if needed.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two women live on the same street, but live 1.5 miles apart.
Each morning both women begin running at the same time in the same direction. Because of where she lives, Jane is always 1.5 miles ahead of Sue when they start running.
Jane runs at a rate of 6 mph and Sue runs at a rate of 8 mph.
How far from SUE'S house are they when Sue catches up?
Be sure to label your answer. Round to the nearest whole number if needed.
:
let x = distance from S's house when S catches J
then
(x-1.5) = distance run by J when caught
:
Write a time equation, time = dist/speed, both will run the same elapsed time
x%2F8 = %28%28x-1.5%29%29%2F6
Cross multiply
8(x-1.5) = 6x
8x - 12 = 6x
8x - 6x = 12
2x = 12
x = 12/2
x = 6 mi from S's house
:
:
Check this by finding the time of each runner, should be equal
6/8 = .75 hrs
4.5/6 = .75