A car covers four successive  distances at speeds of 10 km/hour, 20 km/hour, 30 km/hour and 60 km/hour respectively. Its average speed over this distance is

Correct option is B

Given:

The car covers four successive distances at speeds of 10 km/h, 20 km/h, 30 km/h, and 60 km/h

Formula Used:

If the distances covered are equal, the average speed is calculated as:

​$$\text{Average Speed} = \frac{n}{\frac{1}{v_1} + \frac{1}{v_2} + \frac{1}{v_3} + \frac{1}{v_4}}$$​​

Where:

n = total number of equal distances,

​$$v_1, v_2, v_3, v_4$$​ = speeds during each segment.

Solution:

1. Substitute the values into the formula:

​$$\text{Average Speed} = \frac{4}{\frac{1}{10} + \frac{1}{20} + \frac{1}{30} + \frac{1}{60}}$$​​

2. Simplify the denominator:

Find the sum of the reciprocals:

​$$\frac{1}{10} + \frac{1}{20} + \frac{1}{30} + \frac{1}{60}$$​​

Find a common denominator (LCM of 10, 20, 30, 60 = 60) and simplify:

​$$\frac{1}{10} = \frac{6}{60}, \frac{1}{20} = \frac{3}{60}, \frac{1}{30} = \frac{2}{60}, \frac{1}{60} = \frac{1}{60}$$​​

​$$\frac{1}{10} + \frac{1}{20} + \frac{1}{30} + \frac{1}{60} = \frac{6}{60} + \frac{3}{60} + \frac{2}{60} + \frac{1}{60} = \frac{12}{60} = \frac{1}{5}$$​​

3. Substitute back into the formula:

​$$\text{Average Speed} = \frac{4}{\frac{1}{5}} = 4 \times 5 = 20 \text{km/h}$$​​

Final Answer:

The average speed over the distance is:

20 km/h