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The answer to the problem—
Six horse ’buses and four motor ’buses travel each hour from Temple Bar to the Bank. The horses take 15 minutes, and the motors 10 minutes on the journey.
If I come to Temple Bar, and wish to reach the Bank as soon as possible, shall I take the first horse ’bus that turns up, or wait for a motor? It must be assumed that I can only see a ’bus as it actually passes me—
is (1) Take a motor if it comes first.
is (2) Take a horse ’bus if it comes first, and comes within 21⁄2 minutes of waiting.
is (3) Wait for a motor if a horse ’bus comes first, but does not come till after 21⁄2 minutes.
As I may have to wait 0 minutes or 15 minutes, the average time of waiting will be 71⁄2 minutes.
If I wait x min., and a horse ’bus arrives, I should reach the Bank in 15 mins, if I took it.
If I waited longer for a motor, which, on the average, will now turn up in 71⁄2 - x mins., I should reach the Bank in 171⁄2 - x mins.
If, therefore, x is greater than 21⁄2, the motor is the quicker.
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