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The distance between cities A and B car ...

The distance between cities A and B car travels from A to B at 60 miles per hour and returns from B to A long the same route at 40 miles per hour. What is the averge speed for the round trip?

A

48

B

50

C

56

D

58

Text Solution

AI Generated Solution

The correct Answer is:
To find the average speed for the round trip from city A to city B and back, we can follow these steps: ### Step-by-Step Solution: 1. **Define the Distance**: Let the distance from city A to city B be \( x \) miles. 2. **Calculate Time for Each Leg of the Trip**: - **From A to B**: The speed is 60 miles per hour. \[ \text{Time for A to B} (t_1) = \frac{\text{Distance}}{\text{Speed}} = \frac{x}{60} \text{ hours} \] - **From B to A**: The speed is 40 miles per hour. \[ \text{Time for B to A} (t_2) = \frac{x}{40} \text{ hours} \] 3. **Calculate Total Time for the Round Trip**: The total time for the round trip is the sum of the time taken for each leg: \[ \text{Total Time} (T) = t_1 + t_2 = \frac{x}{60} + \frac{x}{40} \] To add these fractions, we need a common denominator. The least common multiple of 60 and 40 is 120. \[ T = \frac{x}{60} + \frac{x}{40} = \frac{2x}{120} + \frac{3x}{120} = \frac{5x}{120} = \frac{x}{24} \text{ hours} \] 4. **Calculate Total Distance for the Round Trip**: The total distance for the round trip is: \[ \text{Total Distance} = x + x = 2x \text{ miles} \] 5. **Calculate Average Speed**: The average speed is defined as total distance divided by total time: \[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2x}{\frac{x}{24}} = 2x \times \frac{24}{x} = 48 \text{ miles per hour} \] ### Final Answer: The average speed for the round trip is **48 miles per hour**. ---
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