Question 975934: Fred originally ran a 42km marathon in 3 hours. Fred wants to improve his net time by six minutes next year. He will try a different strategy of running for the first two hours at a certain (but unknown) speed, and then completing the rest of the race at a rate 2 kilometres per hour faster than this speed.
If he is to succeed, what is the speed will he need to run for the first two hours of next year’s marathon?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Fred originally ran a 42km marathon in 3 hours.
Fred wants to improve his net time by six minutes next year.
He will try a different strategy of running for the first two hours at a certain (but unknown) speed, and then completing the rest of the race at a rate 2 kilometres per hour faster than this speed.
If he is to succeed, what is the speed will he need to run for the first two hours of next year’s marathon?
:
Find the time (in hrs) of his improved time (6 min less than 3 hrs)
2 + 54/60 = 2.9 hrs
:
Let s = his initial speed
then
(s+2) = finishing speed
:
Write a distance equation: dist = time * speed
:
initial speed dist + finishing speed dist = 42 km
2s + .9(s+2) = 42
2s + .9s + 1.8 = 42
2.9s = 42 - 1.8
2.9s = 40.2
s = 40.2/2.9
s = 13.862 km/hr is his initial speed
:
:
Confirm this by finding the actual dist at each speed.
2(13.862) = 27.724 km
.9(15.862) = 14.276 km (2km faster)
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total dist: 42.000 km
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