Homework math equation setup

Question

* One pipe can fill pool in 9 hours and another pipe can fill the same pool in 12 hours. To fill up the pool, only the first pipe was turned on. After three hours it broke down, and the second pipe was automatically turned on.
a) How many hours did it take to fill up the pool?
b) How many hours would it take to fill up the pool if the two pipes started to work together?

* One truck left town A toward town B. At the same time, a car left town B toward town A. The truck met the car after two hours from the starting time. Then the truck continued for 3 hours and arrived at town B. How many hours did it take the car to cover the distance between two towns?

Answer 1

after 3 hours, the pool was 1/3 full. So the second pipe needs to fill 2/3 of the pool. It would fill the whole pool by itself in 12 hours. So to fill only 2/3 of the pool, it needs (2/3)12 = 8 hours.

 

8 + 3 = 11 hours total

 

each hour the two pipes fill 1/9 + 1/12 = 4/36 + 3/36 = 7/36 of the pool

 

therefore they need 36/7 hours