Question

Jinghua hiked 4 1/2 miles through the woods in 2 1/4 hours. She hiked the return trip at the same average rate but by a different route taking 2 1/2 hours. She hiked the return trip at the same average rate but by a different route taking 2 1/2 hours

Answer 1

5 miles.

Explanation:

Consider the question: Jinghua hiked 4 1/2 miles through the woods in 2 1/4 hours. She hiked the return trip at the same average rate but by a different route taking 2 1/2 hours. How many miles did Jinghua hike on the return trip ?

First of all, we will find Jinghua's speed using given information as:

`\text{Speed}=\frac{\text{Distance}}{\text{Time}}`

Convert mixed fractions into improper fractions:

`4(1)/(2)\Rightarrow (9)/(2)`

`2(1)/(4)\Rightarrow (9)/(4)`

`\text{Jinghua's speed}=\frac{(9)/(2)\text{ Miles}}{(9)/(4)\text{ Hours}}`

Using property
`((a)/(b))/((c)/(d))=(ad)/(bc)`:

`\text{Jinghua's speed}=\frac{9*4\text{ Miles}}{9*2\text{ Hours}}`

`\text{Jinghua's speed}=\frac{2\text{ Miles}}{\text{ Hour}}`

We know that distance is equal to the product of speed and time.

`\text{Distance}=\text{Speed}*\text{Time}`

Since we have been given that Jingua hiked the return trip at the same average rate, so distance covered by her on return trip would be speed (2 miles her hour) times given time (2 1/2 hours).

`\text{Distance covered by Jingua on return trip}=\frac{2\text{ Miles}}{\text{ Hour}}* 2(1)/(2)\text{ Hours}`

`\text{Distance covered by Jingua on return trip}=2\text{ Miles}* (5)/(2)`

`\text{Distance covered by Jingua on return trip}=5\text{ Miles}`

Therefore, Jingua hiked 5 miles on her return trip.