Full solution

Q. A car made a

60

mile trip at an average speed of

20

mph. On the return trip, the car’s average speed was

30

mph. What was the average speed of the car for the entire two-way trip?

Calculate time to destination: Calculate the time taken for the trip to the destination. $\newline$ We know the distance to the destination is $60$ miles and the average speed going there is $20$ mph. To find the time, we use the formula $\text{time} = \frac{\text{distance}}{\text{speed}}$ . $\newline$ Time to destination = $\frac{60 \text{ miles}}{20 \text{ mph}} = 3$ hours.
Calculate time for return trip: Calculate the time taken for the return trip. $\newline$ The distance for the return trip is the same, $60$ miles, but the average speed on the return trip is $30$ mph. Again, we use the formula $\text{time} = \frac{\text{distance}}{\text{speed}}$ . $\newline$ Time for return trip = $\frac{60 \text{ miles}}{30 \text{ mph}} = 2$ hours.
Calculate total time for two-way trip: Calculate the total time for the entire two-way trip. $\newline$ Total time $= \text{Time to destination} + \text{Time for return trip}$ $\newline$ Total time $= 3 \text{ hours} + 2 \text{ hours} = 5 \text{ hours}.$
Calculate total distance for two-way trip: Calculate the total distance for the entire two-way trip. $\newline$ Total distance $= \text{Distance to destination} + \text{Distance for return trip}$ $\newline$ Total distance $= 60 \text{ miles} + 60 \text{ miles} = 120 \text{ miles}.$
Calculate average speed for two-way trip: Calculate the average speed for the entire two-way trip. $\newline$ The average speed is the total distance divided by the total time. We use the formula average speed $= \frac{\text{total distance}}{\text{total time}}$ . $\newline$ Average speed $= \frac{120 \, \text{miles}}{5 \, \text{hours}} = 24 \, \text{mph}$ .