SOLUTION: Alex is a faster runner than Bob. Alex runs 3 yards every second. Bob runs 2.5 yards every second. Alex gives Bob a 30 yard head start in a race, and reaches the finish line exa

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Question 401313: Alex is a faster runner than Bob. Alex runs 3 yards every second. Bob runs 2.5 yards every second. Alex gives Bob a 30 yard head start in a race, and reaches the finish line exactly 2 seconds before Bob. How many yards did Alex run?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Alex is a faster runner than Bob. Alex runs 3 yards every second.
Bob runs 2.5 yards every second.
Alex gives Bob a 30 yard head start in a race, and reaches the finish line exactly 2 seconds before Bob.
How many yards did Alex run?
:
Let d = distance run by Alex
then
(d-30) = distance run by Bob (after Alex starts)
:
Write a time equation, Time = dist/speed
:
Bob's time - Alex's time = 2 sec
%28%28d-30%29%29%2F2.5 - d%2F3 = 2 sec
Multiply eq by 15
15*%28%28d-30%29%29%2F2.5 - 15*d%2F3 = 15(2)
Cancel denominators, results:
6(d-30) - 5d = 30
6d - 180 - 5d = 30
6d - 5d = 30 + 180
d = 210 yds run by Alex
:
:
Check by finding the actual time of each; (Bob runs 210 - 30 = 180 yds)
180/2.5 = 72 seconds
210/3.0 = 70 seconds
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difference 2 seconds