Chapter 11.4, Problem 44PPE

a.

To determine

The expression that represent the total time spend rowing.

Answer to Problem 44PPE

  $\frac{18}{5u}$

Explanation of Solution

Given information:

A rowing team practices rowing 2 mi upstream and 2 mi downstream. The team can row downstream 25% faster than they can row upstream.

Concept used:

The formula for the distance traveled is $d=rt$

Calculation:

Let the team’s rate rowing upstream be u . Then the rate at which the team can row downstream would be $1.25u$ as they can row downstream 25% faster than to upstream.

Now in order to find the expression that represents the total time, use the time-distance formula with the given values as shown below

  $\begin{array}{c}\text{Total time}=\text{Time rowing downstream + Time rowing upstream}\\ \text{=}\frac{\text{Distance traveled}}{\text{Speed downstream}}+\frac{\text{Distance traveled}}{\text{Speed upstream}}\\ =\frac{2}{1.25u}+\frac{2}{u}\\ =\frac{2}{1.25u}+\frac{2}{u}\cdot \frac{1.25}{1.25}\\ =\frac{2}{1.25u}+\frac{2.5}{1.25u}\\ =\frac{2+2.5}{1.25u}\\ =\frac{4.5}{1.25u}\\ =\frac{18}{5u}\end{array}$

Thus, the expression for total time is $\frac{18}{5u}$ .

b.

To determine

The expression that represent the total time spend rowing.

Answer to Problem 44PPE

  $\frac{18}{5d}$

Explanation of Solution

Given information:

A rowing team practices rowing 2 mi upstream and 2 mi downstream. The team can row downstream 25% faster than they can row upstream.

Concept used:

The formula for the distance traveled is $d=rt$

Calculation:

Let the team’s rate rowing upstream be d . Then the rate at which the team can row downstream would be $1.25d$ as they can row downstream 25% faster than to upstream.

Now in order to find the expression that represents the total time, use the time-distance formula with the given values as shown below

  $\begin{array}{c}\text{Total time}=\text{Time rowing downstream + Time rowing upstream}\\ \text{=}\frac{\text{Distance traveled}}{\text{Speed downstream}}+\frac{\text{Distance traveled}}{\text{Speed upstream}}\\ =\frac{2}{1.25d}+\frac{2}{d}\\ =\frac{2}{1.25d}+\frac{2}{d}\cdot \frac{1.25}{1.25}\\ =\frac{2}{1.25d}+\frac{2.5}{1.25d}\\ =\frac{2+2.5}{1.25d}\\ =\frac{4.5}{1.25d}\\ =\frac{18}{5d}\end{array}$

Thus, the expression for total time is $\frac{18}{5d}$ .

c.

To determine

Whether the expressions in (a) and (b) represent the same time.

Answer to Problem 44PPE

  $\text{Yes}$

Explanation of Solution

Given information:

A rowing team practices rowing 2 mi upstream and 2 mi downstream. The team can row downstream 25% faster than they can row upstream.

Concept used:

The formula for the distance traveled is $d=rt$

Calculation:

Only the variable changed to represent the rate at which the team’s row, so it doesn’t change anything in the total time spend in rowing.