Chapter 8.4, Problem 5E

a.

To determine

To calculate: the time each person would take working alone, if they worked at the same rate.

Answer to Problem 5E

Tom and Sue would individually take $\text{6 h}$ to complete the task if their working rate is same.

Explanation of Solution

Given:

Tom and Sue can complete a task in $3\text{ h}$ . Working alone Sue takes $\text{5 h}$ .

Calculation:

As per the given problem,

Considering the work rate of Tom and Sue is the same, that is, they take equal hours to complete the task.

Tom and Sue together can complete the task in $3\text{ h}$

Alone they would complete the task in double the time, that is, $2\times 3\text{ h}=\text{6 h}$

b.

To determine

To infer:Sue’s actual time is greater than or less than the answer obtained in part (a).

Then draw conclusion about Tom’s time working alone.

Answer to Problem 5E

Sue’s actual time is less than the answer obtained in part (a).

By this, it can be concluded that Tom takes more time than Sue to complete the task alone.

Explanation of Solution

Given:

Tom and Sue can complete a task in $3\text{ h}$ . Working alone Sue takes $\text{5 h}$ .

Calculation:

As per the problem,

Sue takes $\text{5 h}$ to complete the work alone.

Sue would individually take $\text{6 h}$ to complete the task if her working rate is same as Tom’s. (as obtained in part(a))

Thus, Sue’s actual time is less than the answer obtained in part (a).

By this, it can be concluded that Tom’s actual work rate is less than that of Sue’s, that is, Tom takes more time than Sue to complete the task alone.

c.

To determine

To find:Tom’s time working alone and compare with the answer obtained in part (b).

Answer to Problem 5E

Tom takes $7.5\text{ h}$ to complete the task alone, which is correct according the conclusions drawn in part (b).

Explanation of Solution

Given:

Tom and Sue can complete a task in $3\text{ h}$ . Working alone Sue takes $\text{5 h}$ .

Calculation:

As per the problem,

Let Tom complete the work alone in $x\text{ h}$

So, part of the work Tom completes in one hour $=\frac{1}{x}$

Sue takes $\text{5 h}$ to complete the work alone.

So, part of work Sue completes in one hour $=\frac{1}{5}$

Together, Tom and Sue can complete the task in $3\text{ h}$ .

So., part of the work completed in one hour by them $=\frac{1}{3}$

Equating the work done by Sue and Tom individually to the work done by them together in one hour:

  $\begin{array}{l}\frac{1}{x}+\frac{1}{5}=\frac{1}{3}\\ \frac{1}{x}=\frac{1}{3}-\frac{1}{5}\\ \frac{1}{x}=\frac{5-3}{15}\\ \frac{1}{x}=\frac{2}{15}\\ x=\frac{15}{2}=7.5\end{array}$

Therefore, Tom takes $7.5\text{ h}$ to complete the task alone, which is correct according the conclusions drawn in part (b).