posted by david on .
3.An 1145 L tank contains 295 L of water and is being filled with brine from a full 1280 L tank at a rate of 1.55 U.S. gallons every 6 seconds. Will the smaller tank ever contain three times the amount of liquid as the larger tank? If so, when? If not, explain why.
After t seconds, we want
295+1.55*t/6 = 3(1280 - 1.55*t/6)
t = 3430.6
after 3430.6 seconds, 886.2 gallons have drained
295+886.2 = 1181.2
1280-886.2 = 393.8
If the smaller tank were big enough to hold enough, after 3430.6 seconds it would hold 3 times the fluid of the larger tank.
However, it's too small, so we need to check to see when the larger tank has drained to 1145/3 gallons.
That occurs after 3477.4 seconds. It takes longer, because the small tank overflows, and the larger tank has to drain longer.
If the smaller tank is sealed, then it will never hold 3 times as much as the larger tank, because flow will stop too soon.