Question

A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is fi ve feet nine, wants to cover a distance of one mile by jumping. If this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump, how many jumps it would take this athlete to jump one mile?

Answer 1

46 jumps

Explanation:

Since the grasshopper is two inches long, and can jump a distance of 40 inches, then its jump ratio is 2:40 = 1:20.

The athlete's body-length is 5 feet 9 inches. We convert this to inches which is 5 × 12 = 60 inches. We then add the remaining 9 inches to make it 60 + 9 = 69 inches. Since our jump ratio for the grasshopper equals that for the athlete, 1:20 = 69: 20 × 69= 69 : 1380. Thus the athlete's jump ratio is 69 inches to 1380 inches.

The athlete wants to cover one mile and we know that 1 mile = 63360 inches. So, we divide the distance the athlete wants to cover(1 mile = 63360 inches) by his jump-length(1380 inches) to get the number of jumps it takes to cover a mile. Number of jumps × jump-length of athlete = one mile, so Number of jumps = one mile/jump-length of athlete = 63360 inches/ 1380 inches= 45.9 jumps ≈ 46 jumps.