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?
<pre></pre>
4 leaps of the thief are as long as 3 leaps of the policeman.
<pre>
Suppose 4 thief-leaps = 3 policeman-leaps = 12 feet

Then each thief-leap = 3 feet, and each policeman-leap = 4 feet
</pre>
The thief takes 6 leaps while the policeman is taking 5 leaps
<pre>
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.

</pre>
A policeman is pursuing a thief who is ahead by 72 of his own leaps.
<pre>
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</pre>