A truck driver, once in a week, leaves his house and drives to the river dock to pick up supplies. At 6:05 PM, one-fifth of the way to the dock, he passes the Temple. At 6:15 PM, one-third of the way, he passes the Dhaba. At what time does he reach the dock?  

Given Data:

At 6:05 PM, he is one-fifth (1/5) of the way.

At 6:15 PM, he is one-third (1/3) of the way.

Concept:

The time it takes to travel between the specified fractions of the total distance can be equated to the corresponding fractions of the total travel time.

Solution:

⇒ The driver traveled from 1/5 to 1/3 of the total distance from 6:05 PM to 6:15 PM, which is 10 minutes.

⇒ The fraction of the journey completed in this 10 minutes is 1/3 - 1/5 = 2/15.

⇒ Therefore, the total time for the journey can be calculated using the proportion, 10 minutes is to 2/15 as Total time is to 1 (the whole journey).

⇒ So, Total time = (10 minutes / 2/15) = 75 minutes.

⇒ The start time of the journey is therefore 6:05 PM - (1/5 of total time) = 6:05PM - (75 minutes / 5) = 6:05 PM - 15 minutes = 5:50 PM.

⇒ Adding the total time to the start of the journey to get the time the driver reaches the dock, we get 5:50 PM + 75 minutes = 7:05 PM.

Therefore, the driver reaches the dock at 7:05 PM.