Question

Working together, two pumps can drain a certain pool in 5 hours. If it takes the older pump 15 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own? Do not do any rounding.

Answer 1

the new pump can drain the pool on its own in 7.5 h

Explanation:

denoting each pump capacity as C , t as the time required to pump the pool , V as the volume of the pool and 1 and 2 for old and new pump respectively , we have that

C₁*t₁=V

(C₁+C₂)*t₃ = V

then we have that

(C₁+C₂)*t₃ = C₁*t₁

C₁*t₃ + C₂*t₃ = C₁*t₁

C₂*t₃ = C₁*t₁ - C₁*t₃

C₂ = C₁ ( t₁ -t₃)/t₃

then the time required for the newer pump to drain the pool is

C₂ *t₂= V

C₂ *t₂ = C₁*t₁

t₂ = C₁*t₁ / C₂

replacing C₂

t₂ = C₁*t₁ / [ C₁ ( t₁ -t₃)/t₃ ] = t₁*t₃/( t₁ -t₃)

t₂ = t₁*t₃/( t₁ -t₃)

where t₁ = time required for the old pump to drain the pool and t₁ = time required for the both pumps to drain the pool

replacing values

t₂ = t₁*t₃/( t₁ -t₃) = 5 h * 15 h /(15 h - 5 h ) = 7.5 h

then the new pump can drain the pool on its own in 7.5 h