26 Arithmetic & Algebraic Problems- THE THREE CARS
Three cars travelling along a road in the same direction are, at a certain
moment, in the following positions in relation to one another. Andrews is a
certain distance behind Brooks, and Carter is twice that distance in front of
Brooks. Each car travels at its own uniform rate of speed, with the result that
Andrews passes Brooks in seven minutes, and passes Carter five minutes later.
In how many minutes after Andrews would Brooks pass Carter?
86. THE FLY AND THE CARS
A road is 300 miles long. A car, A, starts at noon from one end and goes
throughout at 50 miles an hour, and at the same time another car, B, going
uniformly at 100 miles an hour, starts from the other end together with a fly
travelling 150 miles an hour. When the fly meets car A, it immediately turns
and flies towards B.
(1) When does the fly meet B?
The fly then turns towards A and continues flying backwards and forwards
between A and B.
(2) When will the fly be crushed between the two cars if they collide and it
does not get out of the way?
- THE SUBWAY STAIRS
We ran up against Percy Longman, a young athlete, the other day when
leaving Curley Street subway station. He stopped at the elevator, saying,
"I always go up by the stairs. A bit of exercise, you know. But this is the long-
est stairway on the line-nearly a thousand steps. I will tell you a queer thing
about it that only applies to one other smaller stairway on the line. If I go up
two steps at a time, there is one step left for the last bound; if I go up three
at a time, there are two steps left; ifl go up four at a time, there are three steps
left; five at a time, four are left; six at a time, five are left; and if I went up
seven at a time there would be six steps left over for the last bound. Now,
why is that?"
As he went flying up the stairs, three steps at a time, we laughed and said,
"He little suspects that if he went up twenty steps at a time there would be