I need some help with a word problem?

Question

A distillate flows into an empty 64-gallon drum at spout A and out of the drum at spout B. If the rate of flow through A is 2 gallons per hour, how many gallons per hour must flow out at spout B so that the drum is full in exactly 96 hours?
the answer is 4/3 but I don't know how they got it

? · Accepted Answer

Let x = number of gallons per hour flowing out of spout B.

Since 2 gallons per hour are flowing into the drum, the net increase

per hour is 2 - x gallons.

Since it takes 96 hours to fill the 64-gallon drum,

at the rate of 2 - x gallons per hour,

this produces the equation

96(2 - x) = 64.  Solving, we get

x = 4/3

ranjankar · Answer

Let the flow out from spout B  be  x  gallons per hour

Then when both are on the drum fills at the rate of ( 2-x) gallons per hour

So in 96 hours the inflow is  96 ( 2-x)  =  64

192 - 96x = 64

96x = 128

x = 128/96 = 8/6 = 4/3  gallons per hour ANSWER

CHECK

2 -4/3 = 2/3

64 / 2/3 = 96 hours

shadowjack · Answer

they did this 64 times 2/96 then simplified it by dividing by 32 from both top and bottom and came up with 4/3

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I need some help with a word problem?

3 Answers