Machine A can assemble a product in 9 hours while machine B can assemble the same product in 7 hours. How long (in hr) does it take to assemble the product if both machines work together?

Answer 1

Machine A can assemble 1/9 of the product in 1 hour

Machine B can assemble 1/7 of the product in 1 hour

Together they can assemble 1/9 + 1/7 = 7/63 + 9/63 = 16/63 of product in 1 hour

So will take 63/16 hours to assemble whole product together = 3.9375 ~ 4 hours.

Answer 2

Let

a = 9 hr be the amount of time it takes machine A do the job,

b = 7 hr be the amount of time it takes machine B do the job,

x be the amount of time it takes both machines do the job.

In 1 hour machine A assembles 1/a fraction of the product,

machine B assembles 1/b fraction of the product,

machines A and B together woulkd assemble 1/x fraction of the product.

Also we can say that machines A and B together assemble 1/a + 1/b.

Therefore

1/x = 1/a + 1/b

x = 1/(1/a + 1/b) = a b / (a + b)

Substituting actual numbers:

x = 9 x 7 / (9 + 7) = 3.9 hr