Dunman High Prelims 2008 P1 Q8
A swimming pool can be filled by a large pipe operating alone in 3 hours. If the pool is filled by the small pipe alone, it will take t hours longer than the larger pipe filling it alone. And it will take 2 hours for both pipes to fill up the pool. Find the value of t.
*************************
Answer:
Operating alone, the large pipe fills 1/3 of the swimming pool in 1 hour.
Operating alone, the small pipe fills 1/(3+t) of the swimming pool in 1 hour.
Operating together, two pipes fill 1/3 + 1/(3+t) of the swimming pool in 1 hour.
Since it takes 2 hours for both pipes to fill up the pool, both pipes will fill 1/2 of the pool in 1 hour.
Hence, 1/3 + 1/(3+t) = 1/2
1/(3+t) = 1/2 - 1/3
1/(3+t) = 1/6
3+t = 6
hence, t = 3
