Working simultaneously at the respective constant rates,

Cydney Seigerman, Magoosh Tutor

Hi Parijat :)

Good question! We are expressing the rates in this problem as nails/hour. Since we're told that Machines A and B produce 800 nails in x hours, the rate is

800 nails / x hours = 800/x nails/hour

Likewise, we're told that Machine A produces 800 nails in y hours:

800 nails / y hours = 800/y nails/hour

On the other hand, if we had been told that the two machines produce 1 nails every x hours and Machine A produced 1 nail every y hours, we would have the following rates:

Machines A and B: 1/x nails/hours
Machine A: 1/y nails/hours

As you can see, the rates depend on the information provided in the question. The units are nails/hours, so we have the number of nails in the numerator and the number of hours it takes to produce that number of nails in the denominator :)

I hope this clears up your doubts!

Jun 10, 2016 • Reply