Question

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?

Answer 1

The repairman takes approximately 5.625 minutes to fix one pair of shoes by himself.

Step-by-step explanation:

Let x be the amount of time it takes for the repairman to fix one pair of shoes.

Since the assistant takes twice as long, their time can be represented as 2x.

Together, the repairman and assistant can fix 16 pairs of shoes in 8 hours, so their combined rate is 16 pairs / 8 hours = 2 pairs per hour.

Using the formula: Rate × Time = Work, we can set up the equation: (1/x + 1/(2x)) × 8 = 16.

Multiplying both sides by 2x to eliminate the fractions, we get: 2 + 1 = 32x.

Combining like terms, we have: 3 = 32x.

Dividing both sides by 32, we find: x = 3/32.

Therefore, it takes the repairman 3/32 of an hour, or approximately 5.625 minutes, to fix one pair of shoes by himself.

Answer 2

`\boxed{\boxed{Answer: \tex{ }$45$ minutes}}`

Hello!

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

Call x the repair speed of the assistant. Then, the repair speed of the repairman is 2x, and the joint speed is 2x + x = 3x.

Also, the joint speed is 16 pairs in 8 hours = 16 pairs/ 8 hours = 2 pairs/hour.

Thus, we can equate:

`3x = 2 pairs/hour, \text { or } x = (2/3) pairs / hour.$\\`

That is the speed of the assistant. Then, the speed of the repairman is:

`2x = 2 (2/3) pairs/hour\\2x = (4/3) pairs/hour.`

That means that the repairman takes the inverse of 4/3 of an hour to repair one pair of shoes. That is 3/4 of an hour (to repair on pair)

• 3/4 of an hour is 45 minutes and this is the answer.