SOLUTION: A policeman is pursuing a thief who is ahead by 72 of his own leaps. The thief takes 6 leaps while the policeman is taking 5 leaps, but 4 leaps of the thief are as long as 3 leaps

Question 975054: A policeman is pursuing a thief who is ahead by 72 of his own leaps. The thief takes 6 leaps while the policeman is taking 5 leaps, but 4 leaps of the thief are as long as 3 leaps of the policeman. How many leaps will the policeman make before the thief is caught?
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
A policeman is pursuing a thief who is ahead by 72 of his own leaps. The thief
takes 6 leaps while the policeman is taking 5 leaps, but 4 leaps of the thief
are as long as 3 leaps of the policeman. How many leaps will the policeman make
before the thief is caught?

4 leaps of the thief are as long as 3 leaps of the policeman.

Suppose 4 thief-leaps = 3 policeman-leaps = 12 feet

Then each thief-leap = 3 feet, and each policeman-leap = 4 feet

The thief takes 6 leaps while the policeman is taking 5 leaps

So the thief runs 6x3=18 feet while the policeman runs 5x4=20 feet.

Suppose the thief runs 18 feet/second and the policeman runs 20 ft/sec. 

Then the policeman's catch-up rate is 20-18 = 2 ft/sec.

A policeman is pursuing a thief who is ahead by 72 of his own leaps.

72 policeman-leaps = 72x4 = 288 feet.

We calculate the time it will take the policeman to catch up those 288 feet
at the rate of 2 ft/sec:

time = distance/rate = 288/2 = 144 seconds.

Since distance = rate x time, he will go 20x144 = 2880 feet.

Since each policeman-leap is 12 feet, then 2880/12 = 240 leaps.

Edwin

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