The Johnson family traveled 126 miles from Greenville to Harrison in 2 hours and 40 minutes. They left…

Question

The Johnson family traveled 126 miles from Greenville to Harrison in 2 hours and 40 minutes. They left Greenville at 09:15. Calculate their average speed and arrival time.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the Johnson family's trip.

3.1.1 The family took 2 hours and 40 minutes to travel from Greenville to Harrison. Calculate the average speed, to the nearest mile per hour (mph), of the family during the trip. Show ALL calculations.

Convert the total travel time to hours.
$40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours}$ $\text{Total time} = 2 \text{ hours} + \frac{2}{3} \text{ hours} = \frac{6}{3} \text{ hours} + \frac{2}{3} \text{ hours} = \frac{8}{3} \text{ hours} \approx 2.6667 \text{ hours}$
Use the formula $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ .
$\text{Speed} = \frac{126 \text{ miles}}{\frac{8}{3} \text{ hours}} = \frac{126 \times 3}{8} \text{ mph} = \frac{378}{8} \text{ mph} = 47.25 \text{ mph}$
Round the average speed to the nearest mile per hour.
$\text{Average speed} \approx \boxed{47 \text{ mph}}$
3.1.2 The family left Greenville at 09:15 in the morning. Using the time from QUESTION 3.1.1, calculate the time at which the family arrived in Harrison. Show all working and give your final answer in hours and minutes.
Add the travel time to the departure time.
Departure time: 09:15
Travel time: 2 hours 40 minutes
Add the hours.
$09 \text{ hours} + 2 \text{ hours} = 11 \text{ hours}$
Add the minutes.
$15 \text{ minutes} + 40 \text{ minutes} = 55 \text{ minutes}$
Combine hours and minutes to find the arrival time.
$\text{Arrival time} = \boxed{11:55}$
3.1.3 Explain why the actual travel time of a journey is often longer than the calculated time using a map and speed alone. Give TWO reasons.
1. Traffic and Road Conditions: The calculated time assumes ideal driving conditions. In reality, traffic congestion, road construction, accidents, or adverse weather can significantly slow down travel, increasing the actual time taken.
2. Stops and Breaks: Journeys often include planned or unplanned stops for fuel, food, restroom breaks, or simply to rest. These stops add to the total duration of the trip but are not factored into a simple distance/speed calculation.

The Johnson family traveled 126 miles from Greenville to Harrison in 2 hours and 40 minutes. They left Greenville at 09:15. Calculate their average speed and arrival time.

Answer

Step-by-step solution

Convert the total travel time to hours.

Use the formula $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ .

Round the average speed to the nearest mile per hour.

Add the travel time to the departure time.

Add the hours.

Add the minutes.

Combine hours and minutes to find the arrival time.

Try one yourself

Still stuck on this one?

More Mathematics Questions

The Johnson family traveled 126 miles from Greenville to Harrison in 2 hours and 40 minutes. They left Greenville at 09:15. Calculate their average speed and arrival time.

Answer

Step-by-step solution

Convert the total travel time to hours.

Use the formula Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}Speed=TimeDistance​.

Round the average speed to the nearest mile per hour.

Add the travel time to the departure time.

Add the hours.

Add the minutes.

Combine hours and minutes to find the arrival time.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Use the formula $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ .