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.

Question

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

We need to set up an equation that relates the distances Amir hiked at different speeds to the total distance of 5 miles.

Let:

• \( t \) be the time spent hiking during the second part of the hike (at 1.5 miles per hour).
• The time spent hiking during the first part will then be \( 2 - t \) hours (since the total time is 2 hours).

Amir's speed for the first part of the hike is 3 miles per hour, so the distance he hiked in that part is given by the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Thus, the distance for the first part is: \[ 3(2 - t) \] miles.

For the second part of the hike, where he hikes at 1.5 miles per hour for \( t \) hours, the distance he covers is: \[ 1.5t \] miles.

The total distance he hiked is 5 miles, so we can set up the following equation: \[ 3(2 - t) + 1.5t = 5. \]

Therefore, the correct equation to find \( t \) is: 3(2 – t) + 1.5t = 5.