A girl goes to school at a speed of 45 km/h. She comes back with a speed of 36 km/h. Find her average speed for the whole journey.
40 km/h
To find the average speed for the whole journey, we need to understand that the average speed is calculated based on the total distance traveled and the total time taken. Here, the girl travels to school and returns back, making her trip consist of two legs with different speeds.
Let's assume the distance from her home to school (one way) is d km.
- Time taken to go to school at 45 km/h: \(\frac{d}{45}\) hours
- Time taken to return from school at 36 km/h: \(\frac{d}{36}\) hours
- Total distance for the round trip: 2d km
- Total time for the round trip: \(\frac{d}{45} + \frac{d}{36}\) hours
To find a common denominator for the time expressions, we calculate:
- \(\frac{d}{45} + \frac{d}{36} = d\left(\frac{1}{45} + \frac{1}{36}\right)\)
- Common denominator for 45 and 36 is 180, so: \(\frac{1}{45} = \frac{4}{180}, \frac{1}{36} = \frac{5}{180}\)
- \(\frac{1}{45} + \frac{1}{36} = \frac{4}{180} + \frac{5}{180} = \frac{9}{180} = \frac{1}{20}\)
- Total time: d\frac{1}{20} = \frac{d}{20}\) hours
Finally, the average speed V_{avg} is given by:
V_{avg} = \frac{\text{Total distance}}{\text{Total time}} = \frac{2d}{\frac{d}{20}} = 2d \times \frac{20}{d} = 40 \, \text{km/h}
Thus, the average speed for the whole journey is 40 km/h.
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Important Questions from Average Speed
A person covers a certain distance at the speed of 60 kmph and returns to the starting point at a speed of 40 kmph . Find the average speed (in km/hour) of the person for the whole journey.
A train runs at a speed of 28 kmph for 4 hours and 30 kmph for 5 hours and the remaining 40 kms in one hour. What is the average speed per hour?
Kapil travels for 4.5 hours at a speed of 50 km / h and 7.5 hours at a speed of 70 km / h. At the end of it, he finds that he covered only 6/7 of the total distance. At what average speed should he travel so that the remaining distance traveled in 5 hours?
A car has to cover 125 kms in 5 hours. What will be the average speed of the car if it has covered 90 kms in the first 3 hours?
A scooter from P to Q travels at 40 km/h and from Q to P at 30 km/h. What is the average speed of the scooter?
