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Water from 2 hoses of different diameters can fill a swimming pool in 4 hours when used simultaneously.
If each hose is used separately it takes 6 hours longer to fill the pool with the smaller diameter hose than with the larger diameter hose.
Suppose the time taken to fill the pool using only the smaller diameter hose is T hours.
(i) what fraction of the pool is filled in 4 hours by the smaller diameter hose?
(ii) what fraction of the pool is filled in 4 hours by the larger diameter hose?
iii form an equation and solve it to find the time taken to fill the pool if only the smaller diameter hose is used.
Let the completed job (full pool) = 1
Multiply each term by T(T-6), to get rid of the denominators
4T + 4(T-6) = T(T-6)
4T + 4T - 24 = T^2 - 6T
8T - 24 = T^2 - 6t
Form a quadratic equation on the right
0 = T^2 - 6t - 8t + 24
T^2 - 14t + 24 = 0
Factors easily to:
(T-2)(T-12) = 0
Only solution that makes sense
T = 12 hrs for the small pipe is used
Check solution in original equation