One pump can empty a pool in 4 days, whereas a second pump can empty the pool in 10 days. how long will it take the two pumps, working together, to empty the pool? (fractional answers are ok.)

20/7 days (just less than 3 days)

Step-by-step explanation:

Recall that (1 job) = (rate)(time), so time = (1 job) / (rate).

Set up and solve the following equation:

  1 job

= time required for 2 pumps working together

1 job         1 job

+

4 days      10 days

This comes out to:

              1 job

= time required

10 job-days      4 job-days

+

   40 days           40 days

or:

    1 job

= (40/14) days, or 20/7 days (just less than 3 days)

14 job·days

   40 days  

incomplete question. how do you expect anyone to you when you do not post the question in its entirety?

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)