Chapter 7.5, Problem 34E

(a)

To determine

To complete: The given table.

Answer to Problem 34E

The complete table is shown in table (1).

Explanation of Solution

Given:

It will take 2 hours to clean the park when working alone.

It will take 1.2 hours to clean the park when working together.

Calculation:

Let $t$ be the time taken by the friend to clean the park.

First complete the table as follows.

	Work rate	Time	Work done
You	$\frac{\text{1}\text{park}}{2\text{hours}}$	$1.2$ hours	$\frac{\text{1}\text{.2}}{\text{2}}$
Friend	$\frac{\text{1}\text{park}}{t\text{hours}}$	$1.2$ hours	$\frac{\text{1}\text{.2}}{t}$

Table (1)

Therefore, the complete table is shown in table (1).

(b)

To determine

To explain: The sum of the expressions represents in the last column, write and solve an equation to find the time taken by friend to clean the park.

Answer to Problem 34E

It would take 3 hours to clean the park.

Explanation of Solution

Given:

It will take 2 hours to clean the park when working alone.

It will take 1.2 hours to clean the park when working together.

Calculation:

Let $t$ be the time taken by the friend to clean the park.

The sum is the amount of time it would take you and your friend to work together.

  $\begin{array}{c}\frac{1.2}{2}+\frac{1.2}{t}=1\\ 1.2t+2.4=2t\\ 0.8t=2.4\\ t=3\text{hours}\end{array}$

Therefore, it would take 3 hours to clean the park.