Question

A new machine can produce two more engine parts in an hour than an old machine. Therefore, the new machine finished a certain job in 7 hours while the old one needed 8 hours to produce the same number of engine parts. How many parts did the new machine produce in an hour?

Answer 1

For this type of problems, we try to work with the rate of production per unit time.

Let
x=rate of production of old machine (parts/hour)
x+2=rate of production of new machine  (parts/hour)

"the new machine finished a certain job in 7 hours while the old one needed 8 hours to produce the same number of engine parts. "  
means
7(x+2) = 8x
Solve for x
8x-7x=14
x=14 parts/hour (rate of old machine)
x+2=16 parts/hour (rate of new machine)

Check:  7(14+2)=112, 8(14)=112  ✔