Taxies leave station X for station Y every 10 min. Simultaneously, a taxi also leave station Y for station X every 10 min. The taxies move at the same constant speedand go from X to Y or vice-versa in 2h. How many taxies coming from the other side will meat each taxi enroute from Y to X?

a.24 b. 23 c.12 d. 11 (single correct)

To solve the problem of how many taxis will meet each taxi en route from station Y to station X, we need to analyze the situation step by step. Let's break it down clearly.

Understanding the Journey

Both taxis leave their respective stations every 10 minutes and travel at the same constant speed. The total travel time from one station to the other is 2 hours (or 120 minutes).

Calculating the Number of Taxis on the Route

First, let’s determine how many taxis are on the road at any given time. Since taxis leave every 10 minutes, we can calculate how many taxis are on the route from each station during the 2-hour journey.

• In 120 minutes, a taxi leaves every 10 minutes, so:
• Number of taxis leaving from each station = 120 minutes / 10 minutes = 12 taxis.

Therefore, at any point in time, there are 12 taxis traveling from X to Y and 12 taxis traveling from Y to X.

Meeting Points on the Route

Now, let’s focus on a specific taxi that is traveling from Y to X. This taxi will meet other taxis that are traveling from X to Y. Since the taxi from Y to X takes 2 hours to reach its destination, we need to consider the taxis that are already on the road when it starts its journey.

Timing of the Taxis

When the taxi leaves Y, it will encounter:

Calculating the Additional Taxis

During the 2-hour journey, the taxi from Y to X will meet:

Final Count of Taxis Encountered

Now, we can add the two groups of taxis together:

• 12 taxis already on the road + 12 taxis that leave during the journey = 24 taxis.

Thus, the total number of taxis that the taxi from Y to X will meet is 24. Therefore, the correct answer is a. 24.