A car travels from point A to point B at a speed of 60 mph and returns to point A at a speed of 80 mph. What is the average speed for the round trip?
Question
A car travels from point A to point B at a speed of 60 mph and returns to point A at a speed of 80 mph. What is the average speed for the round trip?
Solution
To calculate the average speed for the round trip, we need to consider the total distance traveled and the total time taken.
Step 1: Calculate the total distance The car travels from point A to point B and then returns to point A. So, the total distance covered is twice the distance from A to B. Let's denote the distance from A to B as 'd'. So, the total distance = 2d.
Step 2: Calculate the total time taken The time taken to travel from A to B = distance/speed = d/60 hours. The time taken to return from B to A = d/80 hours. So, the total time taken = d/60 + d/80.
Step 3: Calculate the average speed The average speed = total distance / total time = 2d / (d/60 + d/80).
To simplify this, you can find a common denominator for the fractions in the denominator of the right side: = 2d / [(4d + 3d) / (240)] = 2d / [(7d) / 240] = 2d * (240/7d) = 480/7 mph = approximately 68.57 mph.
So, the average speed for the round trip is approximately 68.57 mph.
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