Question

A vessel having 30 m² 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 m'/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:

A vessel having 30 m² 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 m'/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 2

Given:

The volume of vessel = 30m³

The rate of water flow through the smaller opening = U m³/hr

The rate of water flow through the larger opening = V m³/hr

Relation between U and V: 3U+2V=70

The time of emptying = 1 hour

To Find:

The value of V

Solution:

From the given equation 3U+2V=70,

2V = 70- 3U

or V = 70- 3U / 2         - (1)

Since in 1 hour whole of the tank is emptied,

⇒ The amount of water flowing through both the openings in 1 hour should equal 30m³.

⇒ U + V = 30

or V = 30 - U          - (2)

Solving equations (1) and (2) by substituting the value of U from (1) in (2)

V = 30 - (70 - 2V / 3)

3V = 90 - 70 + 2v

or V = 90 - 70

or V = 20

Hence, the rate at which water is flowing through the larger opening is 20 m³/hr.