SOLUTION: A tank can be filled by two taps A and B in 33 and 1/3 minutes (33 minutes and 20 seconds) when they are running together. Tap A running by itself fills the tank in 15 minutes less

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A tank can be filled by two taps A and B in 33 and 1/3 minutes (33 minutes and 20 seconds) when they are running together. Tap A running by itself fills the tank in 15 minutes less      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 937747: A tank can be filled by two taps A and B in 33 and 1/3 minutes (33 minutes and 20 seconds) when they are running together. Tap A running by itself fills the tank in 15 minutes less than tap B. Find the time taken for each tap running by itself to fill the tank.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A tank can be filled by two taps A and B in 33 and 1/3 minutes (33 minutes and 20 seconds) when they are running together. Tap A running by itself fills the tank in 15 minutes less than tap B. Find the time taken for each tap running by itself to fill the tank.
---------
Together DATA: time = 100/3 min/job ; rate = 3/100 job/min
---------------
Tap A DATA: time = x-15 min/job ; rate = 1/(x-15) job/min
-----
Tap B DATA: time = x min/job ; rate = 1/x job/min
-------------------------
Equation:
rate + rate = together rate
-------
1/x + 1/(x-15) = 3/100
------
100(x-15)+100x = 3x(x-15)
200x - 1500 = 3x^2 - 45x
-----
3x^2 -245x + 1500 = 0
Positive solution::
x = 75 minutes (time for Tap B to do the job)
x-15 = 60 min (time for Tap A to do the job)
---------------
Cheers,
Stan H.
---------------