SOLUTION: 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

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)
----------------------
total dist: 42.000 km
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