Question

Jake can mulch a garden in 30 minutes. together, jake and ross can mulch the same garden in 16 minutes. how much time t, in minutes, will ti take ross to mulch the garden when working alone?

Answer 1

"Jake can mulch a garden in 30 minutes." So, for 1 min Jake can mulch 1/30 part of a garden.

Ross can mulch the park for x minutes. So, for 1 min Jake can mulch 1/x part of a garden.

If they work together, for 1 min they will mulch (1/30 + 1/x) part of the garden.

At the same time, we know, that of they work together they can mulch the garden in 16 min, so for 1 min they will mulch 1/16 part of the garden.

Now, we can write an equation

$\frac{1}{30} + \frac{1}{x} = \frac{1}{16} \\ \\ \frac{1}{x} = \frac{1}{16} - \frac{1}{30} \\ \\ \frac{1}{x} =\frac{30-16}{16*30} \\ \\ \frac{1}{x} =\frac{14}{16*30} \\ \\x=\frac{16*30}{14}$

x≈34.3 (min)

Answer 2

The time taken for ross to mulch the garden when working alone is 34.3 minutes.

• The calculation is as follows:

$\frac{1}{30} + \frac{1}{x} = \frac{1}{16}\\\\ \frac{1}{x} = \frac{1}{16} - \frac{1}{30}\\\\ \frac{1}{x} = \frac{30- 16 }{30\times 16} \\\\x = \frac{16\times 30}{14}$

= 34.3 minutes

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