Question

A man travels for 6 hours at a rate of 50 miles per hour. His return trip takes him 15/2 hours. What is his average speed for the whole trip?

Answer 1

To find the average speed for the whole trip, we first need to determine the total distance traveled and the total time taken.

**Step 1: Calculate the distance for the first part of the trip.**
The man travels for 6 hours at a speed of 50 miles per hour.
Distance = Speed × Time = 50 miles/hour × 6 hours = 300 miles.

**Step 2: Calculate the time taken for the return trip.**
The return trip takes him \( \frac{15}{2} \) hours, which is equal to 7.5 hours.

**Step 3: Calculate the distance for the return trip.**
Since the return trip is straight back, the distance is the same: 300 miles.

**Step 4: Calculate the total distance.**
Total distance = Distance going + Distance returning = 300 miles + 300 miles = 600 miles.

**Step 5: Calculate the total time.**
Total time = Time going + Time returning = 6 hours + 7.5 hours = 13.5 hours.

**Step 6: Calculate the average speed for the whole trip.**
Average Speed = Total Distance / Total Time = 600 miles / 13.5 hours.

Now, calculating \( \frac{600}{13.5} \):

\[
\frac{600}{13.5} = 44.4444... \text{ miles per hour}
\]

To express this as a fraction:

600 ÷ 13.5 = 600 ÷ \frac{27}{2} = 600 × \frac{2}{27} = \frac{1200}{27} = \frac{400}{9} \text{ miles per hour}

Finally, rounding it, we find that the average speed for the whole trip is:

\[
\text{Average Speed} \approx 44.44 \text{ miles/hour}
\]
Thus,

\[
\text{Final Result: } \frac{400}{9} \text{ miles/hour} \approx 44.44 \text{ miles/hour}
\]