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A car made a 6060 mile trip at an average speed of 2020 mph. On the return trip, the car’s average speed was 3030 mph. What was the average speed of the car for the entire two-way trip?

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Q. A car made a 6060 mile trip at an average speed of 2020 mph. On the return trip, the car’s average speed was 3030 mph. What was the average speed of the car for the entire two-way trip?
  1. Calculate time to destination: Calculate the time taken for the trip to the destination.\newlineWe know the distance to the destination is 6060 miles and the average speed going there is 2020 mph. To find the time, we use the formula time=distancespeed\text{time} = \frac{\text{distance}}{\text{speed}}.\newlineTime to destination = 60 miles20 mph=3\frac{60 \text{ miles}}{20 \text{ mph}} = 3 hours.
  2. Calculate time for return trip: Calculate the time taken for the return trip.\newlineThe distance for the return trip is the same, 6060 miles, but the average speed on the return trip is 3030 mph. Again, we use the formula time=distancespeed\text{time} = \frac{\text{distance}}{\text{speed}}.\newlineTime for return trip = 60 miles30 mph=2\frac{60 \text{ miles}}{30 \text{ mph}} = 2 hours.
  3. Calculate total time for two-way trip: Calculate the total time for the entire two-way trip.\newlineTotal time =Time to destination+Time for return trip= \text{Time to destination} + \text{Time for return trip}\newlineTotal time =3 hours+2 hours=5 hours.= 3 \text{ hours} + 2 \text{ hours} = 5 \text{ hours}.
  4. Calculate total distance for two-way trip: Calculate the total distance for the entire two-way trip.\newlineTotal distance =Distance to destination+Distance for return trip= \text{Distance to destination} + \text{Distance for return trip}\newlineTotal distance =60 miles+60 miles=120 miles.= 60 \text{ miles} + 60 \text{ miles} = 120 \text{ miles}.
  5. Calculate average speed for two-way trip: Calculate the average speed for the entire two-way trip.\newlineThe average speed is the total distance divided by the total time. We use the formula average speed =total distancetotal time= \frac{\text{total distance}}{\text{total time}}.\newlineAverage speed =120 miles5 hours=24 mph= \frac{120 \, \text{miles}}{5 \, \text{hours}} = 24 \, \text{mph}.

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