A motorist completes a journey of 1330 km in 14 hours. What is his average speed in kilometers per hour? How long will it take to cover a distance of 570 km at the same average spe... A motorist completes a journey of 1330 km in 14 hours. What is his average speed in kilometers per hour? How long will it take to cover a distance of 570 km at the same average speed?

Understand the Problem

The question involves calculating average speed and using it to determine the time taken to cover a different distance. First, we need to calculate the average speed using the given total distance and time. Then, using this average speed, we'll find the time required to cover the new distance.

Answer

3 hours and 45 minutes
Answer for screen readers

3 hours and 45 minutes

Steps to Solve

  1. Convert time to hours

Convert 2 hours and 30 minutes to hours. Since 30 minutes is half an hour, we have:

$2 \text{ hours } 30 \text{ minutes} = 2 + \frac{30}{60} = 2 + 0.5 = 2.5 \text{ hours}$

  1. Calculate average speed

Average speed is calculated by dividing the total distance by the total time.

$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$

$\text{Average Speed} = \frac{120 \text{ miles}}{2.5 \text{ hours}} = 48 \text{ miles per hour}$

  1. Calculate time to travel 180 miles

Now, we need to find the time it takes to travel 180 miles at the same average speed. We can rearrange the average speed formula to solve for time:

$\text{Time} = \frac{\text{Distance}}{\text{Average Speed}}$

$\text{Time} = \frac{180 \text{ miles}}{48 \text{ miles per hour}} = 3.75 \text{ hours}$

  1. Convert time to hours and minutes

Convert 3.75 hours to hours and minutes. The whole number part is the hours, and the decimal part needs to be converted to minutes.

$0.75 \text{ hours} = 0.75 \times 60 \text{ minutes} = 45 \text{ minutes}$

So, $3.75 \text{ hours} = 3 \text{ hours } 45 \text{ minutes}$

3 hours and 45 minutes

More Information

The train's average speed is 48 miles per hour. At this speed, it will take the train 3 hours and 45 minutes to travel 180 miles.

Tips

A common mistake is failing to convert the initial time into a single unit (hours) or forgetting to convert the final time from decimal hours back into hours and minutes. Also, students may incorrectly apply the formula for average speed or rearrange it incorrectly when solving for time.

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