pipe A alone can fill ONE tank in 6 hours more than it takes pipe B alone to fill ONE tank. Together both pipes can fill ONE tank in 4 hrs. How long will it take each pipe alone to fill ONE tank?
Make this chart
number time filling
of tanks required rate in
filled in hours tanks/hr
pipe A alone
pipe B alone
both togther
and since we are talking only about filling ONE tank, we put
1 for the number of tanks filled in all three cases:
number time filling
of tanks required rate in
filled in hours tanks/hr
pipe A alone 1
pipe B alone 1
both togther 1
We are asked how long it will take each pipe alone to fill ONE tank.
Let x = number of hours it will take pipe B alone to fill ONE tank.
>>...pipe A alone can fill ONE tank in 6 hours more than it takes
pipe B alone to fill ONE tank...<<
So x+6 = number of hours it will take pipe A alone to fill the tank.
number time filling
of tanks required rate in
filled in hours tanks/hr
pipe A alone 1 x+6
pipe B alone 1 x
both togther 1
>>...Together both pipes can fill ONE tank in 4 hrs...<<
So fill in 4 for the time reequired for both together:
number time filling
of tanks required rate in
filled in hours tanks/hr
pipe A alone 1 x+6
pipe B alone 1 x
both togther 1 4
Now fill in the three rates in tanks/hr by dividing
the number of tanks by the hours:
number time filling
of tanks required rate in
filled in hours tanks/hr
pipe A alone 1 x+6 1/(x+6)
pipe B alone 1 x 1/x
both togther 1 4 1/4
The equation comes from
So the equation is
To solve that you clear of fractions and simplify to
a quadratic equation. Then you get two solutions and
discard the negative one and get
x = 6, which is how many hours it would take pipe B
And we add 6 to that,
x+6 = 12, which is how many hours it would take pipe A
Edwin
