A group of 10 students are on
a field trip when their bus
breaks down 40 miles away
from the school.
A teacher takes 5 of them
back to school in her car,
travelling at an average speed
of 40 miles per hour.
The other 5 students start
walking towards school at a
steady 4miles per hour. The
teacher drops the 5
at school, then immediately
turns around and comes back
for the others, again travelling
at a steady speed of 40
miles per hour.
How far have the students
walked by the time the car
reaches them?
What a lot of unnecessary "verbage" !
What does it matter if there are 10 students or 12 or ... ?
No wonder some students find math difficult.
let the distance walked by the students be x
then time spent by students walking = x/4 hours
in that same time, the teacher went (40 + 40-x) miles at 40 mph
so time = (80 - x)/40
x/4 = (80-x)/40
40x = 320 - 4x
44x = 320
x = 11/80 miles or appr 7.27 miles
Thank you so much. I asked one of my friends to explain it to me the other day but I was so confused. Thank you.
To find out how far the students have walked by the time the car reaches them, we need to calculate the time it takes for the car to reach them.
The distance between the bus breakdown location and the school is 40 miles.
The teacher takes 5 students in her car and travels at an average speed of 40 miles per hour. Therefore, the time it takes for the car to reach the school is:
Time = Distance / Speed
Time = 40 miles / 40 miles per hour
Time = 1 hour
Since the car immediately turns around and comes back for the other 5 students at the same speed of 40 miles per hour, it will take another 1 hour for the car to reach them.
Therefore, by the time the car reaches the students, they have walked for 2 hours.
Now, let's calculate the distance they have walked:
The 5 students started walking at a steady speed of 4 miles per hour.
Distance = Speed x Time
Distance = 4 miles per hour x 2 hours
Distance = 8 miles
So, the students have walked a distance of 8 miles by the time the car reaches them.
To determine how far the students have walked by the time the car reaches them, we need to consider the time it takes for the car to travel to the students.
The distance between the broken-down bus and the school is 40 miles. The teacher takes 5 students back to the school in her car, traveling at an average speed of 40 miles per hour. Since the distance traveled is the product of speed and time, we can calculate the time it takes for the car to travel from the broken-down bus to the school.
Time = Distance / Speed
Time = 40 miles / 40 miles per hour
Time = 1 hour
Therefore, it takes 1 hour for the car to reach the school from the broken-down bus.
After dropping off the 5 students at the school, the teacher immediately turns around and comes back for the remaining 5 students. Since the teacher is traveling at a steady speed of 40 miles per hour, it will take the same amount of time (1 hour) to reach the students.
During this time, the 5 students who were left behind have been walking towards the school at a steady speed of 4 miles per hour. To calculate the distance they have covered during this time, we can multiply their speed by the time.
Distance = Speed × Time
Distance = 4 miles per hour × 1 hour
Distance = 4 miles
Therefore, by the time the car reaches the remaining 5 students, they will have walked 4 miles.