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:

(B) 20 m^2

Step-by-step explanation:

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Answer 2

Given:

• Total Volume = 30 $m^3$
• Rate of flow of water through small opening = U $m^3/h$
• Rate of flow of water through large opening = V $m^3/h$
• Given equation = 3U + 2V = 70

To Find:

• The value of V.

Solution:

• We can form an equation using the given data,
• U + V = 30 → (1) and we already have an equation, 3U + 2V = 70 → (2)
• Divide equation (1) by (2) using synthetic division,
•    ( U + V = 30  ) * 3

            3U + 2V = 70

• We get,  3U + 3V = 90

                      - 3U - 2V = -70 (Here, the sign changes)

                      -----------------------

                      3V - 2V = 90 - 70

                                V  = 20

                      ------------------------

• V = 20

∴ The value of V is 20 $m^3/h$ .