Question

An engineer works in a factory out of station. A car is sent for him from the factory every day. The car arrives at the station exactly at the same time as the train. One day the man arrives one hour before his usual time. Without waiting for the car, he starts walking towards the factory. On the way, he meets the car. The man reaches the factory $10$ minutes before the usual time. How long did the engineer walk before he met the car?
A. $40$ minutes
B. $45$ minutes
C. $50$ minutes
D. $55$ minutes

Answer 1

You can approach the solution to this problem by calculating that the engineer had extra 60 minutes to reach the factory and walked for time $t$ and then met the car. And then use the fact that the time saved by the car is actually half the time the engineer reached earlier by, because the car does a to and fro journey.

Complete step-by-step solution:
We will try to solve the question exactly using the approach we suggested in the hint section of the solution to the problem.
First, we need to process the thinking about how to calculate the time the engineer walked.
If we try to analyse the situation, the time that the time that the car saves in total is $10$ minutes. But since the car does a complete journey, time saved by the car in both, to and fro journey is equal and half the time saved by the engineer, so, the time that is saved by the car is only $5$ minutes.
Now, the engineer had an extra 60 minutes, out of which, he walked for $t$ minutes and saved the car $5$ minutes before meeting the car.
Thus, we can write:
$t\, = \,{t_{early}}\, - \,{t_{saved}}$
Where, $t$ is the time the engineer walked for
${t_{early}}$ is the time by which early he reached at the station, i.e. $60$ minutes
And, ${t_{saved}}$ is the time the engineer saved the car in its journey towards the station, which is $5$ minutes.
Now, all we need to do is to substitute the values that we just talked about:
$t\, = \,60\, - \,5 \\\ t\, = \,55 \\\$
So, we can see that the engineer walked for a total of $55$ minutes before meeting the car.
Hence, the correct option is option (D)

Note:- Many students do this question wrong by assuming a certain time taken by the car to reach the station and subtracting the time saved from this, which is a totally wrong approach as the car only saves half the time in each part of its journey. We need to look at this problem using the engineer’s point of view and not the car’s.