Problem Solving

Query : Why does average rate = {total distance/ total time} fail here ?


An adjustable intake valve fills the first 12 gallons of a 24-gallon tank at a rate of 28 gallons per minute. What average rate, in gallons per minute, must the valve allow while filling the remaining 12 gallons in order to have an average rate of 40 gallons per minute for filling the whole tank?

52
60
65
72
70

my take : 40 = 24 / {12/28 + 12/x}
above equation yields x=30 which is wrong.


oa-70

Hi,
you are right.40 = 24 / {12/28 + 12/x}
=>12/28 + 12/x = 12/20 =>1/x = 1/20 - 1/28 = 2/140 = 1/70
so, x= 70.

12/28 + 12/x = 24/40

x= 70

Frankenstein wrote:Hi,
you are right.40 = 24 / {12/28 + 12/x}
=>12/28 + 12/x = 12/20 =>1/x = 1/20 - 1/28 = 2/140 = 1/70
so, x= 70.

bblast wrote:Query : Why does average rate = {total distance/ total time} fail here ?


An adjustable intake valve fills the first 12 gallons of a 24-gallon tank at a rate of 28 gallons per minute. What average rate, in gallons per minute, must the valve allow while filling the remaining 12 gallons in order to have an average rate of 40 gallons per minute for filling the whole tank?

52
60
65
72
70

my take : 40 = 24 / {12/28 + 12/x}
above equation yields x=30 which is wrong.


oa-70

The volume in the tank can be any value -- as long as half of the tank is filled at a rate of 28 gallons per minute, with the whole tank filled at an average rate of 40 gallons per minute.

The LCM of 28 and 40 is 280.
Let tank = 280 gallons.
Time to fill 140 gallons at a rate of 28 gallons per minute = w/r = 140/28 = 5 minutes.
Time to fill 280 gallons at a rate of 40 gallons per minute = 280/40 = 7 minutes.
Thus, time to fill the second half of the tank (140 gallons) = 7-5 = 2 minutes.
Rate needed to fill 140 gallons in 2 minutes = 140/2 = 70.

The correct answer is E.

you can find the total time first- since the overall avg has to be 40G/min, so the avg time = 24/40 mins

Also, we know that for first 12G the total time take is 12/28 mins

To find the time for next 12 G. just subtract the total- initial, which is (24/40)- (12/28) = 12/70.

Therefore, the rate for next 12G is 70G/min.

Answer: E