0 A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is _ five 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?

Question

Mathematics

Kona

15 February, 13:25

0 A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is _ five 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?

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Answers (1)

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Zack Arnold · Answer 1

a) nearest jump is JL = 1380 inches = 115ft

b) number of jumps in 1 mile N = 46 jumps

Step-by-step explanation:

Given that the jump length is proportional to the body length.

If 2 inch grasshopper can jump 40 inches.

JL = k (BL)

k = JL/BL

where JL = jump length = 40 inches

BL = Body length = 2 inches.

k = 40/2 = 20

The constant of proportionality is 20.

For the athlete:

BL = 5ft 9 inches = 5 (12) + 9 = 69 inches.

The jump length of the athlete is:

JL = k (BL) = 20 (69)

JL = 1380 inches. = 115ft

The number of jumps in 1 mile is

1 mile = 63360 inches

N = 63360/1380

N = 45.9 = 46

N = 46

Therefore, 46 jumps would be needed.