Maths Problem?

2020-08-17 6:34 pm

A leaky boat already has some water on board and water is coming in at a constant rate.
Several people are available to operate the manual pumps and, when they do, they all pump
at the same rate. Starting at a given time, five people would take 10 hours to pump the boat
dry, while 12 people would take only 3 hours. How many people are required to pump it dry
in 2 hours from the given time?

回答 (1)

micatkie

2020-08-17 7:37 pm

✔ 最佳答案

Let x vol/h be the rate of water pumped out by 1 people, y vol/h be the rate of water coming in, and z be the volume already on board.
Let n be the number of people required to pump it dry in 2 hours.

5 people take 10 hours to pump the boat dry. 12 people take 3 hours to pump the boat dry. n people take 2 hours to pump the boat dry.
5(10)x = 10y + z …… [1]
12(3)x = 3y + z …… [2]
2nx = 2y + z …… [3]

[1] - [2]:
14x = 7y
2x = y …… [4]

[2] - [3]:
(36 - 2n)x = y …… [5]

[4] = [5]:
2x = (36 - 2n)x
2n = 34
n = 17

Hence, 17 people are required to pump it dry in 2 hours.

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