Math word problem.

Question

It takes an older pump
3

times as long to drain a certain pool as it does a newer pump. Working together, it takes the two pumps
9

hours to drain the pool. How long will it take the older pump to drain the pool working alone?

Do not do any rounding.

Answer 1

Let x=hrs for the older pump to drain the pool

     y=hrs for the newer pump to drain the pool

We have 2 unknowns, so we need 2 equations to solve this problem:

     x=3y

     x+y=9

Using the substitution method, replace "x" with 3y in the 2nd equation and solve for "y":

    x+y=9

   3y+y=9

   4y=9

    y=9/4

Using this value for "y", solve for "x" in the first equation:

    x=3y

    x=3(9/4)

    x=27/4

Check:

   x=3y                         x+y=9

   27/4=3(9/4)              27/4+9/4=9

   27/4=27/4   check     36/4=9

                                   9=9  check

Therefore, the number of hours for the older pump to drain the pool, "x", 27/4=6.75hrs.