Solve

A contractor finds that it takes a crew A 6 hours to construct a wall of a certain size. Crew B takes 8 hours to construct a wall of the same size. How long will it take if they work together?

rate of A crew = wall/6

rate of B crew = wall/8
combined rate = wall/6 + wall/8
= 7wall/24

time with combined rate = wall/(7wall/24)
= 24/7
= 3.428 hours
= 3hours, 25.7 minutes

(notice the effective calculation was 1 ÷ (1/6 + 1/8)

To solve this problem, we can think of the rates at which each crew can complete the task. Let's denote the amount of work required to build the wall as "1".

Crew A's rate of work = 1 wall / 6 hours = 1/6 walls per hour.
Crew B's rate of work = 1 wall / 8 hours = 1/8 walls per hour.

If they work together, we can add their rates of work to find the combined rate. So, the combined rate of work for Crew A and Crew B working together is:

1/6 walls per hour + 1/8 walls per hour = (4/24) walls per hour + (3/24) walls per hour = 7/24 walls per hour.

Now, let's determine how long it would take for them to complete the wall if they work together. We can use the formula: Time = Work / Rate.

Time = 1 wall / (7/24 walls per hour).
Time = 24/7 hours.

Therefore, it would take Crew A and Crew B working together approximately 3.43 hours (or about 3 hours and 26 minutes) to construct the wall.