Question

Elena went on a 6-mile walk. She completed the first half of the walk 1 mi/h faster than usual and the second half of the walk 2 mi/h slower than the first half. If it took 7.2 h to complete the walk, what is her usual rate?

Answer 1

Her usual rate is 0.8333 miles per hour.

Explanation:

The velocity formula is given by:

`v = (d)/(t)`

In which d is the distance and t is the time.

She completed the first half of the walk 1 mi/h faster than usual

Her usual rate is v. 1mph faster is v + 1.

The second half of the walk 2 mi/h slower than the first half.

The first half is v + 1.

2mph slower is v + 1 - 2 = v - 1. Then

Total rate:

7.2 hours, and 6 miles. So

One half is v+1 and the other is v - 1. This is why each is multiplied by 0.5.

`0.5(v + 1) + 0.5(v - 1) = (6)/(7.2)`

`0.5v + 0.5 + 0.5v - 0.5 = 0.8333`

`v = 0.8333`

Her usual rate is 0.8333 miles per hour.