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

The equation that will be used to find t is:

`3(2-t)+1.5t=5`

Explanation:

Total distance that is traveled by Amir is: 5 miles.

and the total time taken by him is: 2 hours.

On the first part of the hike, Amir averaged 3 miles per hour.

Let t denote the time he spent hiking during the second i.e. difficult part of the hike.

• Hence, the time he spent in first part of hike is: 2-t

( Since, the total time was 2 hours)

Also, we know that:

`Distance=Speed* Time`

Hence, distance traveled in first part of hike is:

`Distance=3* (2-t)`

• Now, the distance he will travel in second part of hike will be: 5-3(2-t)

Since the total distance traveled by him is 5 miles.

It is given that his speed decreased to 1.5 miles per hour.

Now, we know that:

`Time=(Distance)/(Speed)`

Hence, time spent by him in second part of hike is:

`t=(5-3(2-t))/(1.5)\\\\i.e.\\\\1.5t=5-3(2-t)\\\\i.e.\\\\3(2-t)+1.5t=5`