Question

Two pipes can together fill a tank in 40/13 minutes. If one pipe take 3 minutes more than the other to fill it, find the time in which each pipe can fill the tank.

Answer 1

let one pipe take x min

then other take x+3 min

two pipes together can fil cistern in 40/13 min

two pipes together can fill 13/40 part of cistern in 1 min

one pipe can fil 1/x part of cister in 1 min

other pipe can fill 1/(x+3) part of cistern in 1 min

a/c to ques.

1/x +1/(x+3) =13/40

(2x+3)40=13(x2+3x)

80x+120=13x2 +39x

0=13x2-41x-120

0=13x2-65x+24x-120

0=13x(x-5) +24(x-5)

0= (x-5)(13x+24)

either, x=5 or, x= -24/13

taking ,x=5

so, first pipe will take 5 mins. whereas, other will take 8 mins.