Work and pipes word problems
The question
How long until the tank is full?
One pipe can fill a tank in 4 hours; a second pipe fills it in 10 hours. Both pipes are opened at once.
+
+ =
+ =
1 ÷ = 2 hours
asked:How long until the tank is full?
2 hours
- Read it through. Two pipes fill the same tank. Times do not add, but how much each does per hour does.
- Work out how much each pipe does in one hour: a pipe that fills the tank in n hours does 1/n of it each hour. Here that is + .
- Together, add them: + = of the tank each hour.
- The two pipes fill of the tank each hour, so the whole tank takes turned over: 1 ÷ = 2 hours.
- Answer the question that was asked — "How long until the tank is full?" — 2 hours.
How it works.
- 01
Read it through. Two pipes fill the same tank. Times do not add, but how much each does per hour does.
- 02
Work out how much each pipe does in one hour: a pipe that fills the tank in n hours does 1/n of it each hour. Here that is 1/4 + 1/10.
- 03
Together, add them: 1/4 + 1/10 = 7/20 of the tank each hour.
- 04
The two pipes fill 7/20 of the tank each hour, so the whole tank takes 7/20 turned over: 1 ÷ 7/20 = 2 6/7 hours.
- 05
Answer the question that was asked — "How long until the tank is full?" — 2 6/7 hours.