Question

A car travels 120 miles from A to B at 30 miles per hour but returns the same distance at 40 miles per hour. The average speed for the round trip is closest to?

Answer 1

The average speed formula is given by:

`\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}`

Let's calculate the total distance first. The car travels 120 miles from point A to point B, and then returns the same distance. Therefore, the total distance is
`\displaystyle\sf 2 * 120 = 240` miles.

Now, let's calculate the total time. The time taken to travel from A to B can be calculated using the formula
`\displaystyle\sf \text{Time} = \frac{\text{Distance}}{\text{Speed}}`.

For the journey from A to B:

`\displaystyle\sf \text{Time}_1 = (120)/(30) = 4` hours

For the return journey from B to A:

`\displaystyle\sf \text{Time}_2 = (120)/(40) = 3` hours

The total time for the round trip is the sum of the individual times:

`\displaystyle\sf \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 4 + 3 = 7` hours

Now, we can calculate the average speed:

`\displaystyle\sf \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = (240)/(7) \approx 34.29` miles per hour.

Therefore, the average speed for the round trip is closest to 34.29 miles per hour.