Question

A worker is digging a ditch . He gets 2 assistants who work 2/3 as fast as he does. If all 3 work on a ditch they should finish it in what fraction of the time that the worker takes working alone.​

Answer 1

Answer:

All 3 working together should finish in $\frac{3}{7}$ of the time that the worker takes working alone.

Step-by-step explanation:

Let's assume that the worker alone could finish the digging work in x days.

Therefore, each day he can complete $\frac{1}{x}$ part of the work.

According to the problem,

each of the two assistants can complete each day $\frac{2}{3} of \frac{1}{x} = \frac{2}{3x}$ part of the work.

If all 3 work on the ditch digging, each day they can complete:

$\frac{1}{x} + 2.\frac{2}{3x}$ part of the work.

$=\frac{1}{x}(1 + \frac{4}{3})$ part of the work.

$=\frac{1}{x}(1 + \frac{4}{3})$ part of the work.

$=\frac{1}{x}(\frac{3+4}{3})$ part of the work.

$=\frac{7}{3x}$ part of the work.

Therefore, all three of they working together can complete the work:

in $\frac{3x}{7} days$

Which is $\frac{\frac{3x}{7} }{x}$ of x $=\frac{3}{7}$ of x.