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

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) (Show Source): You can put this solution on YOUR website!
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
- = 2 sec
Multiply eq by 15
15* - 15* = 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
---------------------
difference 2 seconds

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