Question

Annie is running a trail that is 4 1/2 miles long. She ran the first 2/3 of the distance. Then the trail became very steep, so she slowed down to a walk. Annie walked for 1/2 of the remaining distance and then ran again for the rest of the way. How far did Annie walk? Write the answer as a simplified fraction.

Answer 1

`(3)/(4)` miles

Explanation:

Total length of the trail =
`4(1)/(2)` miles =
`(9)/(2)` miles

She ran the first
`(2)/(3)` of the distance i.e.

The distance for which she ran =
`(2)/(3) * (9)/(2) = 3\ miles`

Remaining distance = Total length of trail minus the distance for which she has already run =
`(9)/(2) - 3 = (3)/(2)` miles

Given that: After running, Annie has to walk due to steep nature of the trail, So, Annie walked for
`(1)/(2)` of the remaining distance.

The distance for which Annie walked =
`(1)/(2) *` Remaining distance

The distance for which Annie walked =
`(1)/(2) *`
`(3)/(2)` =
`(3)/(4)` miles

So, the answer is:
`(3)/(4)` miles