Questions: Suppose you run 4 miles from your house to a friend's house at a speed of 5 miles per hour. When the time comes to return home, you are tired and walk the same 4 miles home at 3 miles per hour. Complete parts (a) through (d) below.

Suppose you run 4 miles from your house to a friend's house at a speed of 5 miles per hour. When the time comes to return home, you are tired and walk the same 4 miles home at 3 miles per hour. Complete parts (a) through (d) below.

Transcript text: Suppose you run 4 miles from your house to a friend's house at a speed of 5 miles per hour. When the time comes to return home, you are tired and walk the same 4 miles home at 3 miles per hour. Complete parts (a) through (d) below.

Solution

Solution Steps

Step 1: Calculate the time spent for each leg of the trip

To calculate the time spent on each leg of the trip, we use the formula \(t = \frac{d}{v}\), where \(d\) is the distance and \(v\) is the speed. For the trip to the destination, \(t_1 = \frac{4}{5} = 0.8\) hours. For the return trip, \(t_2 = \frac{4}{3} = 1.33\) hours.

Step 2: Calculate the total distance and total time

The total distance for the round trip is \(2d = 2 \times 4 = 8\) miles. The total time for the round trip is \(T = t_1 + t_2 = 0.8 + 1.33 = 2.13\) hours.

Step 3: Determine the average speed for the round trip

The average speed for the round trip is calculated using the formula \(V_{avg} = \frac{2d}{T}\), which gives us \(V_{avg} = \frac{2 \times 4}{2.13} = 3.75\) miles per hour.