Question

It took Amir 2 hours to hike 5 miles. On the first part of the hike, Amir averaged 3 miles per hour. For the second part of the hike, the terrain was more difficult so his average speed decreased to 1.5 mile per hour.

Which equation can be used to find t, the amount of time Amir spent hiking during the second, more difficult part of the hike?

3(2 – t) = 1.5t
3t = 1.5(2 – t)
3t + 1.5(2 – t) = 5
3(2 – t) + 1.5t = 5

Answer 1

Let t be the time (in hours) for the second part. Then time for the first part is 2 − t. Distances add to 5:

3(2 − t) + 1.5t = 5.

(You can solve: 6 − 1.5t = 5 → t = 2/3 hour = 40 minutes.)