A shoe repairman is working with his assistant, who takes twice as long to repair a pair of shoes. Together they can fix 16 pairs of shoes in an eight-hour day. How long does it take the repairman to fix one pair of shoes by himself?

Question

Maximo Sanders

Mathematics

23 June, 12:04

A shoe repairman is working with his assistant, who takes twice as long to repair a pair of shoes. Together they can fix 16 pairs of shoes in an eight-hour day. How long does it take the repairman to fix one pair of shoes by himself?

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Answers (1)

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Paul Mendez · Answer 1

The number of pairs of shoes each man can repair is its velocity time the time.

Call x the repair velocity of the assistant. Then, the repair velocity of the repairman is 2x.

So, the number of pairs of shoes that the assitant can repair in an 8 hour day is: x*8 = 8x

And the number of pairs of shoes that the repairman can fix in an 8 hour day is: 2x * 8 = 16x

As per the statement, 16x + 8x = 16

=> 24x = 16 = > x = 16/24 = 2/3 of shoes in 8 hours.

That is the speed of the assistant, while the speed of the repairman is twice that = 4/3 in 8 hours.

So, divide 8 by 4/3 to determine the time to repair one shoe:

8 / (4/3) = 3 * 8 / 4 = 3 * 2 = 6. That, is the repairman will take 6 hours to repair a pair of shoes.

Answer: 6 hours