Question

A motorcyclist covers 4 successive 4 km stretches at speeds of 20 kmph, 30 kmph, 40 kmph, and 50 kmph respectively. Find the average speed over the total distance.

• A.
• B.
• C.
• D.

Hint:

When solving for average speed over multiple stretches, remember that average speed is not the simple arithmetic mean of the speeds. You need to compute the total distance and total time and then divide the total distance by the total time.

Answer 1

The Correct Option is C

Step 1: The total distance covered is 16 km. Step 2: The total time taken is the sum of the times for each of the four stretches. Step 3: The average speed is then calculated using the formula \( \text{average speed} = \frac{\text{total distance}}{\text{total time}} \), yielding approximately 31.2 kmph. \[ \text{Total distance} = 4 + 4 + 4 + 4 = 16 \, \text{km} \] Step 1: Calculate the time taken for each stretch. - Time for the first stretch: \[ \text{Time} = \frac{4}{20} = 0.2 \, \text{hours} \] - Time for the second stretch: \[ \text{Time} = \frac{4}{30} = \frac{2}{15} \, \text{hours} \] - Time for the third stretch: \[ \text{Time} = \frac{4}{40} = 0.1 \, \text{hours} \] - Time for the fourth stretch: \[ \text{Time} = \frac{4}{50} = 0.08 \, \text{hours} \] Step 2: Calculate the total time. \[ \text{Total time} = 0.2 + \frac{2}{15} + 0.1 + 0.08 = 0.2 + 0.1333 + 0.1 + 0.08 = 0.5133 \, \text{hours} \] Step 3: Calculate the average speed. \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{16}{0.5133} \approx 31.2 \, \text{kmph} \]