Question

2. Jane walks one mile from her house to her grandparents' house. Then she returns home,

walking with her grandfather. Her return rate is 75% of her rate walking alone. Let R represent

her rate walking alone

a. Write an expression for the amount of time Jane spends walking.

b. Simplify your expression

c. Suppose Jane's rate walking alone is 4mi/h. About how much time does she spend

walking?

Answer 1

Answer:

a) $\frac{1}{r} + \frac{100}{75r}$

b) $\frac{175}{75r}$

c) 0.583hr or 35 minutes

Step-by-step explanation:

Distance covered by Jane = 1 mile

Let her rate walking alone be r

Return rate = 75% of r

a) Let's find the time spent to and fro using the formula:

$time = \frac{d}{v}$

Time spent going, we have:

d = 1 mile

Speed, v = r

Therefore time spent when going =

$\frac{1}{r}$

Time spend while returning:

d = 1 mile (same distance)

v = 75% of r = $\frac{75}{100} r$

Therefore the time spent while returning = $\frac{1}{\frac{75}{100}*r}}$

$= \frac{100}{75r}$

The amount of time Jane spent walking would be:

$\frac{1}{r} + \frac{100}{75r}$

b) simplifying the expression, we have:

$\frac{1}{r} + \frac{100}{75r}$

Let's take the HCF

$\frac{75 + 100}{75r}$

Let's add the numerator,

$\frac{175}{75r}$

Dividing by 25, we have:

$\frac{175}{75r} = \frac{7}{3r}$

The simplified expression is $\frac{7}{3r}$

c) If her walking rate is 4 mi/hr, the amount of time she would spend walking:

From the simplified exoression, let's substitute 4 for r,$\frac{7}{3r}$

$= \frac{7}{3(4)}$

$= \frac{7}{12} = 0.583$

Converting 0.583 hour to minutes, we have:

0.583 * 60 mins = 35 minutes

Therefore Jane spent 35 minutes walking