Question

Of two inlet pipes, the smaller pipe takes four hours longer than the larger pipe to fill a pool. When both pipes are open, the pool is filled in three hours and forty-five minutes. If only the larger pipe is open, how many hours are required to fill the pool?

Answer 1

Answer:

Let longer pipe take p hr to fill the pool

Then smaller pipe takes p + 4 hr to fill the pool

When both pipes are open it takes 3 hr 45 mts

3hr 45 mts = 3 + (45/60) = 15/4 hr

Longer pipe takes p hr to fill the pool

So in 15/4 hr it will fill (15/4)×(1/p) portion of pool

Smaller pipe takes p+4 hr to fill the pool

So in 15/4 hr it will fill (15/4)×(1/(p+4)) portion of pool

Therefore (15/4)×(1/p) + (15/4)×(1/(p+4)) = 1

(15/4)× (1/p + 1/(p+4)) = 1

1/p + 1/(p+4) = 4/15

(p+4 +p)/{(p×(p+4)} = 4/15

(p + 2)/{p×(p+4)} = 2/15

15×(p+2) = 2×p×(p+4)

2p^2 -7p -30 = 0

2p^2 -12p + 5p -30 =0

2p(p - 6) + 5(p -6) = 0

(2p +5)(p-6) = 0

p-6 = 0

p = 6 hr Ans