The Chief Executive of the Baytein Flit Company sighed as he read the complaint before him.

Dear Sir,
I want to complain about your fly spray – the darn stuff doesn’t work! The other day, me mate drives his truck to the tip at a steady 10 km/h. I follows him an hour later, goin’ at 20 km/h. Just as I leave, I see this great blowie, so I gives him a burst of your spray. He ups and heads for me mate’s truck at a good 25 km/h. When me mate sees him, he gives him a burst from his can, and he comes back to me, not slowed down a bit. Well, I gives him another burst, and off he goes again to me mate’s truck. This goes on until at last I catches up with me mate. Now we have two empty cans, and the *!#? thing is still buzzin’ round me head! Boy, am I mad!
Yours, George Garbo

The Chief Executive smiled as an irrelevant thought crossed his mind. ‘I wonder how far the fly did travel?’ he mused.

Do you know?

Hint 1

Sort out the useful information from the garbage!

Hint 2

Is there more than one way of tackling this problem?

Solution

The useful information is contained in the diagram below.

A first idea might be to try to calculate the total distance travelled by the fly directly. However, this seems to be impossibly difficult. Since only the difference in the speeds of the trucks is significant, we could assume that George’s truck travels at 10 km/h and that his mate’s truck is stationary. This simplifies the problem, but it still appears to be intractable.

A different and more productive approach is to observe that since the fly travels at constant speed, we can determine the distance it travels if we know the length of time it is flying. By comparing the truck speeds, we see that George will catch up with his mate in exactly one hour. Thus the fly is in the air for one hour. Since it is travelling at 25 km/h for one hour, it travels 25 km.

Extensions

Experiment to see if the problem changes when the two trucks are travelling towards each other.
 

What if they travel on perpendicular roads towards a common intersection? Does the fly still travel the same distance?

Hint 1

Hint 2

Solution

Extensions