Problema Solution
If one pump can inflate an air mattress in 33 minutes and a second pump can inflate the same mattress in 99 ​minutes, find the amount of time that would be needed for the two pumps working together to inflate the mattress.
Answer provided by our tutors
Let 'x' represent the time that the pumps need working together to inflate the mattress, x>=0.
1/x mattress per min is the together rate
1/33 mattress per min is the rate of the first pump
1/99 mattress per min is the rate of the second pump
Now we can write the following equation:
1/33 + 1/99 = 1/x
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click here to see the equation solved for x
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x = 24.75 min
x = 24 min 0.75*60 sec
x = 24 min 45 sec
The two pumps working together will need 24 minutes and 45 seconds to inflate the mattress.