Briefly

The potato race

The potato race

In the past, no rural fair was complete without a potato race, and in some locations the hobby is still popular among boys and girls in the countryside.

One hundred potatoes are placed on the ground, in a straight line, ten feet away from each other. A basket is placed ten feet behind the first potato. The two competitors start from the basket and run to the first potato. Who comes first to it takes it to the basket, while the other competitor goes to look for the second.

In this way all the potatoes are transported one by one to the basket, and the winner is the one who first introduces fifty potatoes.

Our first problem is to say How far does a person travel from the basket and pick up the hundred potatoes, one at a time.

Our second problem, much more difficult, concerns a race between Tom and Harry. As Tom is 2.04% faster than Harry, he allows the latter to choose a potato and drop it in the basket before starting the race. In other words, to win the race, Tom must gather fifty potatoes before Harry manages to collect the forty-nine that he lacks.

The illustration shows Harry throwing in the basket the potato he has chosen.

The result of the race will vary according to the potato that Harry chooses. You must determine which potato Harry must choose to maximize his chances of winning and what the outcome of the race will be if he chooses correctly.

Solution

ยกA person must travel 101,000 feet, or a little over 19 miles, to collect the 100 potatoes!

The best strategy for Harry is to choose potato 99. Tom, who is 2.04% faster, will pick up the first potato, Harry the second, Tom the third, and so on until the last.

Tom is not fast enough to pick up two adjacent potatoes. Harry will have to travel 49,980 feet to get his 49 potatoes. During that time, Tom will travel 50,999,592 feet. Since he has to travel 51,000 feet to bring his 50 potatoes,

Harry will win for less than half a foot!