Question

Solve your equation from the first problem and pick the BEST interpretation for the solution. a \large h\approx2.9; The solution shows that it will take about three more hours to fill the pool. b \large h\approx1.8, The solution show that it will take two more hours to fill the pool. c \large h\approx2.9; The solution shows that it will take about 2 more hours to fill the pool. d \large h\approx4.2, The solution shows that it will take 4 more hours to fill the pool.

Answer 1

The correct option is (a).

Explanation:

The complete question is:

A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool.

Solution:

The first hose takes 6 hours to fill the pool.

So, work done per hour by the first hose is, 1/6.

Suppose the second hose takes x hours to fill the pool.

So, work done per hour by the second hose is, 1/x.

The work done per hour by the two hoses together is, [1/6 + 1/x] = (x + 6)/6x.

Together the two hoses can fill the pool in, 6x/(x + 6) hours.

It is provided that, the second hose needs 3 more hours to fill the pool than the two hoses combined.

That is:

6x/(x + 6) = x - 3

6x = (x - 3)(x + 6)

6x = x² + 3x - 18

x² - 3x - 18 = 0

x² - 6x + 3x - 18 = 0

x (x - 6) + 3 (x - 6) = 0

(x + 3)(x - 6) = 0

x = 6

Then the time taken by the two hoses together is,

6x/(x + 6) = x - 3 = 6 - 3 = 3 hours

So, each hose takes 6 hours and together they take 3 hours to fill the pool.

This implies that the second hose takes 3 hours more than the 3 hours together to fill the pool.

Thus, the correct option is (a).