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

a)
`(1)/(r) + (100)/(75r)`

b)
`(175)/(75r)`

c) 0.583hr or 35 minutes

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 = (d)/(v)`

Time spent going, we have:

d = 1 mile

Speed, v = r

Therefore time spent when going =

`(1)/(r)`

Time spend while returning:

d = 1 mile (same distance)

v = 75% of r =
`(75)/(100) r`

Therefore the time spent while returning =
`(1)/((75)/(100)*r)}`

`= (100)/(75r)`

The amount of time Jane spent walking would be:

`(1)/(r) + (100)/(75r)`

b) simplifying the expression, we have:

`(1)/(r) + (100)/(75r)`

Let's take the HCF

`(75 + 100)/(75r)`

Let's add the numerator,

`(175)/(75r)`

Dividing by 25, we have:

`(175)/(75r) = (7)/(3r)`

The simplified expression is
`(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,
`(7)/(3r)`

`= (7)/(3(4))`

`= (7)/(12) = 0.583`

Converting 0.583 hour to minutes, we have:

0.583 * 60 mins = 35 minutes

Therefore Jane spent 35 minutes walking