Henry Ernest Dudeney/Puzzles and Curious Problems/72 - The Fly and the Motor-Cars

Puzzles and Curious Problems by Henry Ernest Dudeney: $72$

The Fly and the Motor-Cars

A road is $300$ miles long.

A motor-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 the 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?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Locomotion and Speed Puzzles: $72$. -- The Fly and the Motor-Cars
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Speed & Distance Puzzles: $86$. The Fly and the Cars