SOLUTION: The liquid fuel tank of a rocket can be filled with one pipe in 6 hours and with another in 8 hours. If both work together for 2 hours. How long would it take the slowest to finish

Click here to see ALL problems on Rate-of-work-word-problems

Question 1162689: The liquid fuel tank of a rocket can be filled with one pipe in 6 hours and with another in 8 hours. If both work together for 2 hours. How long would it take the slowest to finish filling it?
Answer by greenestamps(13209) (Show Source):
You can put this solution on YOUR website!

The faster pipe can fill the tank in 6 hours; in the 2 hours it works, it fills 1/3 of the tank. So the slower pipe fills 2/3 of the tank.

Since the slower pipe can fill the whole tank in 8 hours, it can fill 2/3 of the tank is 2/3 of 8 hours, which is 16/3 hours, or 5 1/3 hours.

So the additional amount of time it takes the slower pipe to fill the tank after the two pipes work together for 2 hours is 3 1/3 hours.

ANSWER: The slower pipe takes 3 1/3 hours to finish filling the tank after the two pipes work together for 2 hours.

Algebraically...

The faster tank fills 1/6 of the tank in 1 hour; the slower fills 1/8 in 1 hour.

The faster pipe working for 2 hours, plus the slower pipe working for 2+x hours, fills the whole tank:

You can solve from there....