Question

A car covers one-third of the distance at a speed of 10 km/h, the second third at 20 km/h, and the last third at 60 km/h. Find the average speed of the car.

• A. 18 km/h
• B. 8 km/h
• C. 20 km/h
• D. 28 km/h

Hint:

To find the average speed when the speed is different for different parts of the trip, use the formula: \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}. \]

Answer 1

The Correct Option is A

Let the total distance be \( D \). The car covers the first third of the distance (\( D/3 \)) at 10 km/h, the second third at 20 km/h, and the last third at 60 km/h. - Time taken for the first third: \[ t_1 = \frac{D/3}{10} \] - Time taken for the second third: \[ t_2 = \frac{D/3}{20} \] - Time taken for the last third: \[ t_3 = \frac{D/3}{60} \] Total time taken: \[ t_{\text{total}} = t_1 + t_2 + t_3 = \frac{D/3}{10} + \frac{D/3}{20} + \frac{D/3}{60} \] Simplify: \[ t_{\text{total}} = \frac{D}{30} + \frac{D}{60} + \frac{D}{180} \] \[ t_{\text{total}} = \frac{6D}{180} + \frac{3D}{180} + \frac{D}{180} = \frac{10D}{180} = \frac{D}{18} \] Average speed is given by: \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{D}{\frac{D}{18}} = 18 \, \text{km/h} \]