Question about two leaking barrels

Question

Two barrels of the same size contains water. They both have a hole at the bottom. One takes 10 hours to finish leaking while the other takes 8 hours. When does one of the barrel contain twice as much water as the other?

Answer 1

At any time x the amount in the barrel is:

 

1 - x/10 for the slow leak

1 - x/8   for the fast leak

 

Slow leak barrel = 2 fast leak barrel

 

1 - x/10 = 2(1 - x/8)           distribute

1 - x/10 = 2 - x/4               add x/4 to both sides

x/4 - x/10 + 1 = 2              subtract 1 form both sides

x/4 - x/10 = 1                    multiply both sides by LCD, 20

5x - 2x = 20                      combine

3x = 20                             divide both sides by 3

x = 6 2/3

 

After six hours forty minutes one barrel (slow leak) contains twice as much as the other barrel (fast leak).