Math Question?
2017-10-28 4:21 am
A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 3 hours, while the outlet pipe can empty it in 7 hours. How long will it take to fill the vat if both pipes are left open? Then, assume that the error was discovered after both pipes have been running for 3 hours and the outlet pipe is closed. How much more time would be required to fill the vat?
回答 (3)
2017-10-28 5:07 am
inflow = 1/3 vat/hour
outflow = 1/7 vat/hour
For the first three hours, the net flow rate into the vat = 1/3 - 1/7 = 4/21 vat/hour
At three hours, the contents of the vat would total 12/21 = 4/7 vat, leaving 3/7 vat to be filled
For the remainder of the fill time, the fill rate would be 1/3 vat/hour which would complete filling the vat in (3/7)/(1/3) = 9/7 hour.
Total time to fill the tank: 4 2/7 hours
Time to fill after the outlet is closed: 1 2/7 hours
My question is what happened to that 3/7 vat of wine that was wasted?
outflow = 1/7 vat/hour
For the first three hours, the net flow rate into the vat = 1/3 - 1/7 = 4/21 vat/hour
At three hours, the contents of the vat would total 12/21 = 4/7 vat, leaving 3/7 vat to be filled
For the remainder of the fill time, the fill rate would be 1/3 vat/hour which would complete filling the vat in (3/7)/(1/3) = 9/7 hour.
Total time to fill the tank: 4 2/7 hours
Time to fill after the outlet is closed: 1 2/7 hours
My question is what happened to that 3/7 vat of wine that was wasted?
2017-10-28 4:33 am
1 / 3 - 1 / 7 = 4 / 21 ===> 21/4 hours to fill.......after 3 hours we see 12 / 21st of the tank is full...leaves 9 / 21 to fill.....[ 9 / 21 ] / [ 1/3] = 9/7 hours to completely fill....total is 4 and 2/7 hours
2017-10-28 4:32 am
In an hour, 1/3 - 1/7 of the vat is filled
= 7/21 - 3/21 = 4/21
Thus the vat fills in 21/4 hours.
After 3 hours, 3*4/21 of the vat is filled = 12/21
That leaves 9/21 of the vat to be filled.
In an hour, the inlet pipe fills 1/3 of the vat.
To fill 9/21 of the vat takes (9/21)/(1/3) hours
= 27/21 hours.
= 7/21 - 3/21 = 4/21
Thus the vat fills in 21/4 hours.
After 3 hours, 3*4/21 of the vat is filled = 12/21
That leaves 9/21 of the vat to be filled.
In an hour, the inlet pipe fills 1/3 of the vat.
To fill 9/21 of the vat takes (9/21)/(1/3) hours
= 27/21 hours.
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