Car travels up hill at a constant speed of 50 km/h and returns down the hill at a constant speed of 65 km/h. Calculate the avg speed for the round trip in km/h.
Let's say the distance 2d is the total distance traveled. It is broken up into two parts. Time is distance divided by speed (km / km/hr = hr).
So, the average velocity v over the whole distance 2d can be found by adding the times for the two halves of the trip
2d/v = d/50 + d/65
2/v = 1/50 + 1/65
It's just a classic work problem in disguise
2/v = 115/3250
v = 2*3250/115 = 56.52 km/h
Just to check, say the trip was 100 km
at 50 km, that's 2 hrs
at 65 km, that's 1.538 hrs.
200 km at 56.52 km/h = 3.538 hrs, the sum of the uphill and downhill times.
To calculate the average speed for the round trip, you need to determine the total distance traveled and the total time taken.
Let's first calculate the distance traveled while going uphill. The speed while traveling uphill is given as 50 km/h. Assuming the time taken to travel uphill is t1 hours, the distance traveled uphill can be calculated using the formula:
Distance uphill = Speed uphill * Time uphill
So, the distance traveled uphill is 50 km/h * t1 hours.
Next, let's calculate the distance traveled while coming down the hill. The speed while traveling downhill is given as 65 km/h. Assuming the time taken to travel downhill is t2 hours, the distance traveled downhill can be calculated using the formula:
Distance downhill = Speed downhill * Time downhill
So, the distance traveled downhill is 65 km/h * t2 hours.
Now, let's calculate the total distance for the round trip. Since the distance traveled uphill is the same as the distance traveled downhill, the total distance for the round trip can be calculated by adding the two distances:
Total distance = Distance uphill + Distance downhill
Total distance = 50 km/h * t1 hours + 65 km/h * t2 hours
The total time for the round trip is the sum of the time taken to travel uphill and the time taken to travel downhill:
Total time = Time uphill + Time downhill
Total time = t1 hours + t2 hours
Finally, to calculate the average speed for the round trip, divide the total distance by the total time:
Average speed = Total distance / Total time
Average speed = (50 km/h * t1 hours + 65 km/h * t2 hours) / (t1 hours + t2 hours)
This formula will give you the average speed for the round trip in km/h.