Jane walks one mile from her house to her grandparents’ house. Then
she returns home, walking with her grandfather. Her return rate is 70% of her normal walking rate. Let r represent her normal walking rate.
a. Write an expression for the amount of time Jane spends walking.
b. Simplify your expression.
since time = distance / speed,
t =1/r + 1/.70r = 1.70/.70r = 2.43/r or 17 / 7r
How did it add up to 1.7/.7r?
a. To write an expression for the amount of time Jane spends walking, we need to consider the distances traveled and the rates of walking.
When Jane walks from her house to her grandparents' house, she covers a distance of one mile. The time taken to cover this distance can be calculated using the formula: Time = Distance / Rate.
Since her normal walking rate is 'r', the time taken to walk from her house to her grandparents' house can be expressed as: Time1 = 1 / r.
When she returns home with her grandfather, her walking rate is 70% of her normal walking rate. This can be calculated by multiplying her normal walking rate 'r' by 0.7. Therefore, her return walking rate is 0.7r.
The time taken to walk back home can be calculated as: Time2 = 1 / (0.7r).
b. To simplify the expression, we can start by rationalizing the denominator of Time2:
Time2 = 1 / (0.7r)
= 1 / (7r/10)
= 10 / 7r
Therefore, the simplified expression for the amount of time Jane spends walking is: Time = Time1 + Time2 = 1/r + 10/7r.
a. To find the expression for the amount of time Jane spends walking, we need to consider both her walk to her grandparents' house and her return walk with her grandfather.
The time it takes Jane to walk one mile to her grandparents' house can be expressed as:
Time for one-way walk = Distance / Rate = 1 / r
The time it takes her to return home with her grandfather is given as 70% of her normal walking rate. So her return rate would be 0.70r. The distance she covers in the return journey is also 1 mile. Hence, the time for the return walk is:
Time for return walk = Distance / Rate = 1 / (0.70r)
b. To simplify the expression, we can start by simplifying the denominator of the expression for the return walk time:
Time for return walk = 1 / (0.70r) = 10/7r
So the simplified expression for the total amount of time Jane spends walking (including the one-way walk and the return walk) is:
Total walking time = Time for one-way walk + Time for return walk
Total walking time = 1/r + 10/7r
To further simplify this expression, we can find the common denominator of r and 7r, which is 7r:
Total walking time = (7/7r) + (10/7r) = (17/7r)
So the simplified expression for the total amount of time Jane spends walking is 17/7r.