word problem

Question

If one pump can inflate an air mattress in 4 minutes and a second pump can inflate the same mattress in 12 ?minutes, find the amount of time that would be needed for the two pumps working together to inflate the mattress.

Answer 1

Pump A can inflate an air mattress in 4 minutes. 

That means in one minute, Pump A can inflate 1/4 of a mattress.

 

Pump B can inflate an air mattress in 12 minutes.

That means in one minute, Pump B can inflate 1/12 of a mattress.

 

So in one minute, Pumps A and B can inflate:

(1/4) + (1/12) of a mattress together

 

1/4 + 1/12

= 3/12 + 1/12

= 4/12

= 1/3 of a mattress in one minute

 

If Pumps A and B together can inflate 1/3 of a mattress in one minute,

it will take 3 minutes to inflate a whole mattress.