Speed and Distance Puzzles on Mental Calculation

A man runs n times round a circular track whose radius is t miles. He drinks s quarts of beer for every mile that he runs. Prove that he will only need one quart!

Nine travellers, each possessing a car, meet on the eastern edge of a desert. They wish to explore the interior, always going due west. Each car can travel forty miles on the contents of the engine tank, which holds a gallon of fuel, and each can carry nine extra gallon cans of fuel and no more. Unopened cans can alone be transferred from car to car. What is the greatest distance at which they can enter the desert without making any depots of fuel for the return journey?

A train is travelling at the rate of sixty miles per hour. A passenger at the back of the train wishes to walk to the front along the corridor and in doing so walks at the rate of three miles per hour. At what rate is the man travelling over the permanent way? We will not involve ourselves here in quibbles and difficulties similar to Zeno’s paradox of the arrow and Einstein’s theory of relativity, but deal with the matter in the simple sense of motion in reference to the permanent way.

A gentleman had to walk to his railway station, four miles from his house, and was encumbered by two bags of equal weight, but too heavy for him to carry alone. His gardener and a boy both insisted on carrying the luggage; but the gardener is an old man and the boy not sufficiently strong, while the gentleman believes in a fair division oflabor and wished to take his own share. They started off with the gardener carrying one bag and the boy the other, while the gentleman worked out the best way of arranging that the three should share the burden equally among them. How would you have managed it?

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?

George treated his best girl to a bus ride, but on account of his limited resources it was necessary that they should walk back. Now, if the bus goes at the rate of nine miles an hour and they walk at the rate of three miles an hour, how far can they ride so that they may be back in eight hours?

“The steamer,” remarked one of our officers home from the East, “was able
to go twenty miles an hour downstream, but could only do fifteen miles an
hour upstream. So, of course, she took five hours longer in coming up than
in going down.”
One could not resist working out mentally the distance from point to point.
What was it?

Colonel Crackham says that his friend, Mr. Wilkinson, walks from his country house into the neighboring town at the rate of five miles per hour, and, because he is a little tired, he makes the return journey at the rate of three miles per hour. The double journey takes him exactly seven hours. Can you tell the distance from his house to the town?

The Crackhams made their first stop at Bugleminster, where they were to spend the night at a friend’s house. This friend was to leave home at the same time and ride to London to put up at the Crackhams’ house. They took the same route, and each car went at its own uniform speed. They kept a look-out for one another, and met forty miles from Bugleminster. George that evening worked out the following little puzzle: “I find that if, on our respective arrivals, we had each at once proceeded on the return, journey at the same speeds we should meet at forty-eight miles from London.” If this were so, what is the distance from London to Bugleminster?

Two cyclists race on a circular track. Brown can ride once round the track in six minutes, and Robinson in four minutes. In how many minutes will Robinson overtake Brown?

A man taking a walk in the country on turning round saw a friend of his walking 400 yards behind in his direction. They each walked 200 yards in a direct line, with their faces towards each other, and you would suppose that they must have met. Yet they found after their 200 yards’ walk that they were still 400 yards apart. Can you explain?

Weary Willie went up a certain hill at the rate of one and a half miles per hour and came down at the rate of four and a half miles per hour, so that it took him just six hours to make the double journey. How far was it to the top of the hill?

A crew can row a certain course upstream in eight and four-sevenths minutes, and, if there were no stream, they could row it in seven minutes less than it takes them to drift down the stream. How long would it take to row down with the stream?

On one of the escalators on the London subway I find that if I walk down twenty-six steps I require thirty seconds to get to the bottom, but if I make thirty-four steps I require only eighteen seconds to reach the bottom. What is the height of the stairway in steps? The time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom onto the level platform.

Referring to the last puzzle, let us now consider the case where a third rider has to share the same bicycle. As a matter of fact, I understand that Anderson and Brown have taken a man named Carter into partnership, and the position today is this: Anderson, Brown, and Carter walk respectively four, five, and three miles per hour, and ride respectively ten, eight, and twelve miles per hour. How are they to use that single bicycle so that all shall complete the twenty miles’ journey at the same time?

If an army forty miles long advances forty miles while a dispatch rider gallops from the rear to the front, delivers a dispatch to the commanding general, and returns to the rear, how far has he to travel?

We were going by train from Anglechester to Clinkerton, and an hour after starting an accident happened to the engine. We had to continue the journey at three-fifths of the former speed. It made us two hours late at Clinkerton, and the driver said that if only the accident had happened fifty miles farther on the train would have arrived forty minutes sooner. Can you tell from that statement just how far it is from Anglechester to Clinkerton?