Mystery Question #7 Answer

Mystery Question:

One night in Deptford, Max was waiting in a house for a burglar to attend. The man appeared as expected, but managed to turn heel and flee. Max shot after him as swiftly as possible. He returned after a short space, with the burglar in tow. Granny enquired as to how difficult it had proven to catch the fellow.

"It was a simple matter," Max replied. "By the time I left the house, he had a 27-step lead, and he was taking eight steps to my five. It would have been bleak, save for the fact that he is a short man, and two of my strides were worth five of his. In fact, from that, you should be able to tell me how many strides I required to apprehend the scoundrel."

Answer:

For every five strides of Max's, the thief was taking eight, but those eight were equivalent to just three and a fifth of the taller man's. So Max was gaining one and four fifths of one of his stride for every five he took. The burglar's 27-stride lead is equivlent to ten and four fifths of Max's strides, and it will take exactly six gains of one and four fifths strides for Max to catch his quarry. 

So Max has to take just 30 paces to catch the villain -who, in that time, will have run a total of 75 steps.