Question 832354
One job is, "empty the tank".

Regular pump, {{{1/6}}} tank per hour
Small pump, {{{1/10}}} tank per hour
Combined, {{{1/6+1/10}}} tank per hour


The combined rate is {{{5/30+3/30=8/30=4/15}}} tank per hour


Your fundamental formula fact: {{{Rate*time=job}}}.


Ignoring time points but just dealing with time lengths,
Total time to empty tank is 4 hours.
Let t = time that pumps operate together.
Regular tank alone for 4-t hours.
The pumps work together for t hours.
'
ACCOUNT FOR THE ONE JOB: {{{highlight((1/6)(4-t)+(4/15)(t)=1)}}}
Solve for t.
Remember, t is a time quantity, NOT a time point.


I am stopping here, so you do the arithmetic steps yourself.  Start by multiplying left and right members of the equation by 30, which will clear the denominators, since lowest common denominator is 30.