A car travels up a hill at a constant speed of 45 km/h and returns down the hill at a constant speed of 70 km/h. Calculate the average speed for the round trip.
To calculate the average speed for the round trip, we need to find the total distance traveled and the total time taken.
Let's first find the distance traveled for the uphill and downhill portions of the trip.
Assuming the distance traveled uphill is 'd' kilometers, the same distance will be covered while traveling downhill.
Since the car travels at a constant speed of 45 km/h uphill and returns at a constant speed of 70 km/h downhill, we can calculate the time taken for each portion.
Time taken for the uphill portion = Distance / Speed = d / 45
Time taken for the downhill portion = Distance / Speed = d / 70
The total time taken for the round trip will be the sum of the time taken for the uphill and downhill portions.
Total time taken = d / 45 + d / 70
To calculate the average speed, we can use the formula:
Average speed = Total distance / Total time
Since the total distance traveled for the round trip is 2d (uphill and downhill), the average speed will be:
Average speed = 2d / (d / 45 + d / 70)
Now, we can simplify this expression to get the average speed for the round trip.