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?

A) 1 1/2 hours
B) 3/4 hours
C) 1/6 hours
D) 1/3 hours

1 answer

Let's say the time it takes for the shoe repairman to fix one pair of shoes by himself is x hours.

The assistant takes twice as long, so it takes him 2x hours to fix one pair of shoes by himself.

Together, they can fix 16 pairs of shoes in 8 hours, so their combined efficiency is 16 pairs of shoes / 8 hours = 2 pairs of shoes per hour.

Since the repairman can fix x pairs of shoes in one hour and the assistant can fix 2x pairs of shoes in one hour, their combined efficiency is x + 2x = 3x pairs of shoes in one hour.

Now we can set up an equation to solve for x:

3x = 2
x = 2/3

So, it takes the repairman 2/3 hours to fix one pair of shoes by himself, which is equivalent to 40 minutes.

Therefore, the answer is D) 1/3 hours.