Question

Two water taps together can fill a tank in one hour and twelve minutes. The tap of smaller diameter takes 1 hour more than the larger one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given Two water taps together can fill a tank in one hour and twelve minutes. The tap of smaller diameter takes 1 hour more than the larger one to fill the tank separately. Find the time in which each tap can separately fill the tank.

• Let tap of smaller diameter be t hrs
• Let tap of bigger diameter be (t – 1) hrs
• In t hrs 1 tank will be full
• So in 1 hr 1/t  of tank will be full
• Now in (t – 1) hr 1 the tank will be full
• So in 1 hr 1/t – 1 part of tank will be full
• So in the same time, in 1 hr it will take 1/t + 1/t – 1
•                                              = t – 1 + t / t(t – 1)
• So in 1 hr it will take 2t – 1 / t (t – 1)
• Now 72 min is taken for 1 tank to be full  
• So for 60 min it will be  60 / 72 = 5/6
• Now equating we get
• 2t – 1 / t (t – 1) = 5/6
• 12t – 6 = 5t (t – 1)
• 12 t – 6 = 5t^2 – 5t
• 5 t^2 – 17 t + 6 = 0
• 5 t^2 – 15 t – 2 t + 6 = 0
• 5 t (t – 3 ) – 2 (t – 3) = 0
• (t – 3) (5 t – 2) = 0
• So t = 3 , t = 2 / 5

So the time taken to fill will be 3 hours