A car travels up a hill at a constant speed of 33 km/h and returns down the hill at a constant speed of 60 km/h. Calculate the average speed (in km/h) for the round trip.
AVG. Speed = (33 + 60) / 2 = 46.5km/h.
To calculate the average speed for the round trip, we need to consider the distance traveled and the time taken for each leg of the trip.
Let's assume the distance traveled up the hill is 'd' km.
Speed = Distance / Time
Given that the car travels up the hill at a constant speed of 33 km/h, we can say that the time taken to travel up the hill is:
Time_up = Distance / Speed_up
Time_up = d km / 33 km/h
Similarly, the car returns down the hill at a constant speed of 60 km/h, so the time taken to return is:
Time_down = Distance / Speed_down
Time_down = d km / 60 km/h
Now, let's calculate the total time taken for the round trip:
Total_time = Time_up + Time_down
Total_time = d km / 33 km/h + d km / 60 km/h
To find the average speed, we can use the formula:
Average_speed = Total_distance / Total_time
Since the total distance traveled is 2d (up and down the hill), we can substitute Total_distance = 2d:
Average_speed = 2d / (d / 33 km/h + d / 60 km/h)
Now, let's simplify the equation:
Average_speed = 2d / (d / 33 + d / 60)
Average_speed = 2d / ((60d + 33d) / (33 * 60))
Average_speed = 2d / (93d / 1980)
Average_speed = (2d * 1980) / 93d
Average_speed = (3960d) / 93d
Average_speed = 42.58 km/h
Therefore, the average speed for the round trip is approximately 42.58 km/h.
To calculate the average speed for the round trip, we need to use the formula:
Average speed = Total distance / Total time
First, we need to determine the total distance traveled.
Let's assume that the distance going up the hill is "x" kilometers. Since the car is traveling at a constant speed of 33 km/h, the time taken to travel up the hill can be calculated using the formula:
Time taken = Distance / Speed
Time taken = x km / 33 km/h
Time taken = x/33 hours
Similarly, the distance going down the hill is also "x" kilometers. Since the car is traveling at a constant speed of 60 km/h, the time taken to travel down the hill can be calculated using the formula:
Time taken = Distance / Speed
Time taken = x km / 60 km/h
Time taken = x/60 hours
The total time of the round trip is the sum of the time going up and the time going down:
Total time = (x/33) + (x/60) hours
We know that the average speed is the total distance divided by the total time:
Average speed = Total distance / Total time
Substituting the equations we derived, we can calculate the average speed:
Average speed = (2x) / [(x/33) + (x/60)] km/h
Simplifying this equation further, we can multiply the numerator and denominator by the least common multiple (LCM) of 33 and 60, which is 660:
Average speed = (2x * 660) / [20x + 11x] km/h
Average speed = (2x * 660) / 31x km/h
Average speed = 1320 / 31 km/h
Therefore, the average speed for the round trip is approximately 42.58 km/h.