Question

A vessel having 30 m3 of water is emptied through two openings, one small and the other large. Water flows out through the smaller opening at the rate of U m3/h and through the larger one at the rate of V m3/h. Given that 3U + 2V = 70 and that the vessel gets fully emptied in 1 hour, what is V?

Answer 1

Answer: V=20 m3/h

Step-by-step explanation:

3u + 2v = 70 (1)

u + v = 30 (2)

(u + v= 30) x -2

3u + 2v = 70

-2u - 2v = -60

u = 10

Substituting the value of  U in (2), we get

10 + v = 30

v = 30 - 10 = 20

Therefore, the rate at which water flows out through the larger opening = 20 m3/h.

Answer 2

Answer: The value of V is $\bold{20\ m^3/h}$.

Given:

• Volume of water is $30 \ m^3$.
• Smaller opening at the rate of $U \ m^3/h$.
• Larger opening at the rate of $V\ m^3/h$.

• 2U + 2v = 70
• Empty time is 1 hour.

To Find: The value of V.

Step-by-step explanation:

As we know that total volume in vessel is $30 \ m^3$ and both opening is opened then vessel gets fully emptied in 1 hour. The rate of opening is showing that how much water will escaped in an hours. So, using this concept we can calculate the volume of water in one hour through small opening and large opening. Thus,

U + V = 30 ...eq(1)

and 3U + 2v = 70 ...eq(2)

From equation (1) we get,

U = 30 - V

Put this value in equation(2) we get,

3 (30 - V) + 2V = 70

90 - 3V + 2V = 70

V = 20 $m^3/h$

Hence correct answer is $20\ m^3/h$.

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