word problem

Question

An aquarium tank can hold6600

liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 66

minutes. The second pipe can fill the tank in 55

minutes by itself. When both pipes are working together, how long does it take them to fill the tank?

Answer 1

These combined rate problems always look hard, but they're generally done in the same way. 

 

You have to change the time it takes for thing (pipe, or person, or whatever) to accomplish the task into the fraction of the task accomplished in each unit of time.  Then add the fractions for each thing together and that gives you the fraction of the task that they can do together in that amount of time.  From that fraction you figure out how much time it takes to complete the whole task when they do it together.

 

So...

 

The first pipe can fill the tank in 66 minutes.  Therefore it completes 1/66 of the task (fills 1/66 of the tank) in 1 minute.

 

Same with the second pipe.  It can fill the tank in 55 minutes, so it complete 1/55 of the task in 1 minute.

 

When they are working together, then in 1 minute they can do 1/66 + 1/55 of the task.  So add 1/55 + 1/66:

 

 1       1

--- +  --- =

55      66

 

66   1       55    1

---  ---  + ---   ---   =

66  55      55    66

 

     66               55

-----------  +  -----------   =

55 * 66          66 * 55

 

   121 

----------  =

66 * 55 

 

     11 * 11

------------------   =

11 * 6 * 11 * 5

 

    1

-------  = 1 / 30.

6 * 5  

 

 

So together they can fill 1/30 of the tank in 1 minute.  Therefore it takes them 30 minutes for them to fill the entire tank.

 

 

Answer 2

This is a basic rate, time problem.

 

rate x time = 1 job

 

Assuming both pipes work at a constant rate,

The first pipe fills 1/66 of the tank in 1 minute.

The second pipe fills 1/55 of the tank in 1 minute.

 

So

1/55 t + 1/66 t = 1

 

Getting a common denominator,

66t/3630 + 55t/3630 = 1

121t/3630 = 1

121t = 3630

 

t = 30 minutes