Question

Dean and his younger brother sam are digging a hole to make imu for the luau. Working together it takes them 1.5 hours to finish the hole. If it would take sat twice as long to finish the hole working alone as it would dean how long would it take dean if he had to dig the hole by himself?

Answer 1

Answer:

Dean can do work alone in 1.5 hours

Step-by-step explanation:

Let x be the no. of hours required by Dean to complete work alone

It would take Sam twice as long to finish the hole working alone as it would dean

So, Sam completes work alone in hours = 2x

Part of work done by Dean in 1 hour = $\frac{1}{x}$

Part of work done by Sam in 1 hour =$\frac{1}{2x}$

Working together they can do part of work in 1 hour = $\frac{1}{x}+ \frac{1}{2x}$

Worming together they finish work in 1.5 hours

So, part of work done together in 1 hour = $\frac{1}{1.5}$

So,$\frac{1}{x}+ \frac{1}{2x}=\frac{1}{1.5}$

$\frac{2x+x}{x(2x)}=\frac{1}{1.5}$

$1.5(3x)=2x^2$

3=2x

1.5=x

So, Dean can do work alone in 1.5 hours