Question

In a certain journey, a man covered one-third of the total distance on a bicycle at the speed of 20 km/h, one-fourth on a bike at the speed of 30 km/h, and the remaining distance at the speed of 50 km/h with a car. What is his average speed during the entire journey?

• A. 30 km/h
• B. 40 km/h
• C. 50 km/h
• D. 60 km/h

Hint:

When calculating average speed, use the formula \( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \). Be sure to account for each part of the journey and use the appropriate time formula for each speed.

Answer 1

The Correct Option is A

Let the total distance be \( D \).
The distance covered on the bicycle is \( \frac{1}{3}D \) at 20 km/h.
The distance covered on the bike is \( \frac{1}{4}D \) at 30 km/h.
The remaining distance covered by car is \( D - \left( \frac{1}{3}D + \frac{1}{4}D \right) = D - \frac{7}{12}D = \frac{5}{12}D \) at 50 km/h.
Now, let's calculate the time taken for each part of the journey:
Time taken on the bicycle = \( \frac{\frac{1}{3}D}{20} = \frac{D}{60} \)
Time taken on the bike = \( \frac{\frac{1}{4}D}{30} = \frac{D}{120} \)
Time taken in the car = \( \frac{\frac{5}{12}D}{50} = \frac{5D}{600} = \frac{D}{120} \)
The total time taken is:
\[ \text{Total Time} = \frac{D}{60} + \frac{D}{120} + \frac{D}{120} = \frac{D}{60} + \frac{2D}{120} = \frac{D}{60} + \frac{D}{60} = \frac{2D}{60} = \frac{D}{30} \] The average speed is the total distance divided by the total time:
\[ \text{Average Speed} = \frac{D}{\frac{D}{30}} = 30 \, \text{km/h} \] Thus, the average speed during the entire journey is \( \boxed{30} \, \text{km/h} \).