Question 1208481: Hi
John and Lester were cycling towards the finish line. 15km from the end John passed Lester. John reached the end 45 minutes earlier than Lester who was still 9km from the end. What was John's speed after overtaking Lester.
Found 3 solutions by ikleyn, greenestamps, MathTherapy:
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
John and Lester were cycling towards the finish line.
15km from the end John passed Lester.
John reached the end 45 minutes earlier than Lester who was still 9 km from the end.
What was John's speed after overtaking Lester?
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From the problem, we may think that John and Lester started simultaneously from the "passing" point,
which is 15 km from the end.
From the problem, we see that Lester spent 45 minutes (or 3/4 of an hour) to cycle 9 kilometers.
Hence, the Lester' speed is  = 12 kilometers per hour.
Cycling with the speed of 12 km/h, Lester spent  =  hours, or 75 minutes, to cover 15 kilometers.
From the problem, John spent 45 minutes less than Lester, i.e. 75-45 = 30 minutes, or 1/2 of an hour.
distance of 15 km
Thus we find the John' speed = ------------------- = 15/(1/2) = 30 kilometers per hour.
time 30 minutes
At this point, the problem is solved completely.
ANSWER. John' speed was 30 kilometers per hour.
Solved.
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This problem is beautiful - I like it very much.
The solution is pure arithmetic; the algebra and equations are not needed.
But the solution requires very accurate and careful analysis of the given data and each used term.
It is really first class (and upper level) arithmetic word problem on Travel and Distance.
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
(1) Lester's speed....
When John finished, Lester was still 9km from the end; and Lester finished 45 minutes (3/4 of an hour) after John. So Lester's speed was  km/hr.
(2) John's speed....
From the time John passed Lester until the time John finished, John cycled 15km while Lester cycled only 15-9 = 6km. So the ratio of their speeds was 15:6 = 5:2.
So John's speed was 5/2 of Lester's: 
ANSWER: John's speed was 30km/hr
Answer by MathTherapy(10556)  (Show Source):
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