A taxi moves at 40 km/h and takes 25 minutes to travel a certain distance. By how many kilometres per hour should it increase its speed in order to cover the same distance in 20 minutes?

Introduction / Context:

This is another time, speed and distance question similar to earlier ones but with different numbers. The taxi initially travels at a given speed and takes a known time to cover a fixed distance. We are asked by how much the speed must be increased so that the same distance is covered in less time. This type of scenario helps you understand inverse relationships between speed and time when distance is constant.

Given Data / Assumptions:

• Initial speed of the taxi = 40 km/h.
• Time taken at this speed = 25 minutes.
• Required time for the same distance = 20 minutes.
• The distance remains the same in both journeys.
• We must find the increase in speed in km/h.

Concept / Approach:

For constant distance, speed and time are inversely proportional. First we compute the distance covered in the initial case by converting time into hours and multiplying by the speed. Next we compute the speed required to cover this same distance in the shorter time. The difference between the new speed and the original speed gives the required increase. Careful unit conversion from minutes to hours is essential to avoid errors.

Step-by-Step Solution:

Verification / Alternative check:

We can check by reasoning with ratios. Time is reduced from 25 minutes to 20 minutes. The ratio of times is 25:20 which simplifies to 5:4. For constant distance, the ratio of speeds must be the inverse, that is 4:5. Therefore the new speed must be 40 * 5/4 = 50 km/h. The difference between 50 and 40 is again 10 km/h, confirming our earlier calculation.

Why Other Options Are Wrong:

Option 50 represents the new speed, not the increase in speed, so it does not directly answer the question. Option 5 km/h and 25 km/h do not correspond to any correct ratio between old and new speed derived from the change in time. They would produce either too small or too large a new speed to achieve the required 20 minute travel time. Only an increase of 10 km/h results in the correct new speed of 50 km/h.

Common Pitfalls:

Students sometimes forget to convert minutes into hours and directly multiply 40 by 25, leading to an incorrect distance. Another mistake is to treat the percentage change in time as the same as the percentage change in speed without using the inverse relationship. It is also possible to confuse the new speed with the increase in speed. Always compute both clearly and then subtract to find the increase.

Final Answer:

The taxi must increase its speed by 10 km/h.