A car travels up a hill at a constant speed of 32 km/h and returns down the hill at a constant speed of 61 km/h. Calculate the average speed
and the answer is not 46.5
To calculate the average speed of the car, we can use the formula:
Average Speed = Total Distance / Total Time
In this case, since the car travels up the hill at one speed and returns down the hill at a different speed, we can consider the distance and time for each leg separately.
Let's assume the distance traveled up the hill is D, and the distance traveled down the hill is also D.
The time it takes to travel up the hill can be calculated by dividing the distance by the speed:
Time up the hill = D / 32 km/h
The time it takes to travel down the hill can be calculated in the same way:
Time down the hill = D / 61 km/h
The total distance traveled is 2D (up and down), and the total time is the sum of the times for each leg:
Total Distance = 2D
Total Time = D / 32 km/h + D / 61 km/h
Now we can substitute these values into the formula for average speed:
Average Speed = Total Distance / Total Time
Average Speed = 2D / (D / 32 km/h + D / 61 km/h)
To simplify this expression, we can find a common denominator for the terms in the denominator:
Average Speed = 2D / ((D * 61) / (32 * 61) km/h + (D * 32) / (32 * 61) km/h)
Average Speed = 2D / ((D * 61 + D * 32) / (32 * 61) km/h)
Average Speed = 2D / ((93D) / (32 * 61) km/h)
Further simplifying:
Average Speed = (2D * 32 * 61) / (93D) km/h
Average Speed = (64D * 61) / (93D) km/h
Average Speed = 3964 / 93 km/h
Calculating this expression, we get:
Average Speed ≈ 42.6 km/h
Therefore, the average speed of the car is approximately 42.6 km/h.