2 pipes together can fill a tank in6 hours 40 minutesfind the each will take to fill the tank, if one of two pipes can fill it in3 hours less than the other :
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Let the time taken by first pipe =xhrs
Time taken by second pipe =x-3hrs
Total time taken =6hrs+40/60hrs
=20/3hrs
Portion of tank filled by first pipe=1/x
Portion of tank filled by second Pipe=1/x-3
20/3(1/x+1/x-3)=1
1/x+1/x-3=3/20
x-3+x/x(x-3)=3/20
2x-3/x^2-3x=3/20
20(2x-3)=3(x^2-3x)
40x-60=3x^2-9x
3x^2-9x-40x+60=0
3x^2-49x+60=0
3x^2-45x-4x+60=0
3x(x-15)-4(x-15)=0
(x-15) (3x-4)=0
x=15 x=4/3
time taken by first pipe is 15hrs
time taken by second pipe is x-3= 15-3=12hrs
Time taken by second pipe =x-3hrs
Total time taken =6hrs+40/60hrs
=20/3hrs
Portion of tank filled by first pipe=1/x
Portion of tank filled by second Pipe=1/x-3
20/3(1/x+1/x-3)=1
1/x+1/x-3=3/20
x-3+x/x(x-3)=3/20
2x-3/x^2-3x=3/20
20(2x-3)=3(x^2-3x)
40x-60=3x^2-9x
3x^2-9x-40x+60=0
3x^2-49x+60=0
3x^2-45x-4x+60=0
3x(x-15)-4(x-15)=0
(x-15) (3x-4)=0
x=15 x=4/3
time taken by first pipe is 15hrs
time taken by second pipe is x-3= 15-3=12hrs
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