On a field trip, a bus breaks down 40 miles from the school. A teacher takes 5 students back to school in her car, traveling at an average speed of 40 miles per hour. The other 5 students start walking towards school at a steady 4 miles per hour.
After dropping the 5 students at school, the teacher immediately turns around and comes back for the others, again traveling at a steady speed of 40 miles per hour.
How far have the students walked by the time the car reaches them?
Answer (2)
We need to calculate how far the walking students have traveled by the time the teacher's car reaches them. First, we determine the time it takes for the teacher to drive the 40 miles to school and then back to the students. Since the teacher is traveling at an average speed of 40 miles per hour (mph), the time to travel 40 miles to school is:
Time = Distance ∕ Speed = 40 miles ∕ 40 mph = 1 hour
The same amount of time is needed for the teacher to travel back, making the total round trip time for the teacher 2 hours. During this time, the remaining 5 students are walking towards the school at 4 miles per hour, so the distance they cover in 2 hours is:
Distance = Speed × Time = 4 mph × 2 hours = 8 miles
Therefore, the students have walked 8 miles by the time the car reaches them.
By the time the teacher's car reaches the walking students, they have walked a total of 8 miles. This distance is calculated based on their walking speed of 4 mph over a 2-hour period. This is due to the teacher taking 1 hour to reach the school and another hour to come back.
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