In driving the usual route to school, a student computes his average speed to be 26 km/h. In a hurry to get home that afternoon, he wants to average 30 km/h for the round trip. What would his average speed for the return trip over the same route have to be in order to do this?
To find the average speed for the return trip, we can use the concept of relative speed.
Let's consider the usual route to school as a one-way distance covered at an average speed of 26 km/h. Since the student wants to average 30 km/h for the round trip, we need to find the average speed for the return trip.
Let's assume the one-way distance from the student's home to school is 'd' kilometers. Therefore, the total distance for the round trip will be '2d' kilometers.
To average 30 km/h for the round trip, the total time taken for the round trip should be '2d/30' hours.
Now, we know that the average speed is calculated by dividing the total distance by the total time.
For the first part of the trip, the student's average speed is 26 km/h. Therefore, the time taken for the first part of the trip is 'd/26' hours.
To find the speed of the return trip, we need to find the time taken for the return trip. The time taken for the return trip can be calculated by subtracting the time taken for the first part of the trip from the total time taken for the round trip.
Time taken for return trip = Total time taken for round trip - Time taken for first part of the trip
Time taken for return trip = 2d/30 - d/26
To find the average speed for the return trip, we divide the total distance (d) by the time taken for the return trip:
Average speed for return trip = Distance / Time taken for return trip
Average speed for return trip = d / (2d/30 - d/26)
Now, we simplify the equation:
Average speed for return trip = d / (2d/30 - d/26)
Average speed for return trip = d / [(52d - 30d) / (780)]
Average speed for return trip = (780d) / (52d - 30d)
Average speed for return trip = (780d) / (22d)
Average speed for return trip = 780 / 22
Average speed for return trip = 35.45 km/h (approximately)
Therefore, the student would need to have an average speed of approximately 35.45 km/h for the return trip in order to average 30 km/h for the round trip.