SOLUTION: Archimedes ran 3 times as fast as his challenger ran. In fact, he ran 60 miles in 3 hours less than it took his challenger to run 32 miles. How fast did each of them run? How long

Question 333783: Archimedes ran 3 times as fast as his challenger ran. In fact, he ran 60 miles in 3 hours less than it took his challenger to run 32 miles. How fast did each of them run? How long did they run?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Archimedes ran 3 times as fast as his challenger ran.
In fact, he ran 60 miles in 3 hours less than it took his challenger to run 32 miles. How fast did each of them run? How long did they run?
:
Let r = running speed of the challenger
then
3r = A's running speed
:
Write a time equation: time = dist/speed
:
challenger's time - A's time = 3 hr
- = 3
Multiply by 3r, results
3(32) - 60 = 3r(3)
:
96 - 60 = 9r
:
9r = 36
r =
r = 4 mph is the challenger's speed
then
3(4) = 12 mph is A/s running speed
:
Find the time for each
32/4 = 8 hrs is challenger's time
60/12 = 5 hrs is A's time
--------------
diff: = 3 hrs, confirms our solutions
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