Question

Three friends Smith, Jack and Pamila are walking at the speed of 3, 4, 5 km/h respectively. They start at the same place at 1, 2, 3 O'clock respectively. When Jack reaches Smith, he sends him back with a message for Pamila. At what time will Pamila get the message?
A. 5:15 O'clock
B. 5:30 O'clock
C. 5:45 O'clock
D. 6:00 O'clock
E. None of these

Answer 1

Hint: To find the time taken to get the message from all the three friends, combine all the time taken to travel per hour of each friend then simplify the distance with respect to time. Hence, by this we can find the total time taken to get the message to pamila.

Complete step by step solution:
Let us write the given data as,
Three friends Smith, Jack and Pamila are walking at the speed of 3, 4, 5 km/h.
The distance travelled by Smith is
\[3 \times 1 = 3km\]
For Jack, time T, when Jack catches Smith
= \[4T - 3T\]= \[3\]
Three as extra distance to be covered by Jack = \[3km\]
Therefore, time T is
\[T = 3hrs\]
After Jack catches Smith, 3hrs have passed and during this time Pamila started walking and has been walking for 2hrs
Thus, Pamila distance travelled by Pamila is
\[5 \times 2 = 10km\].
Now, distance travelled by Smith when he was caught by Jack = \[12km\]
The distance between Pamila and Smith is
\[ = 12km - 10km\]
\[ = 2km\]
Time taken by Smith i.e., \[{T_1}\] to meet Pamila is
\[5{T_1} + 3{T_1} = 2km\]
After simplifying the terms, we get
\[{T_1} = \dfrac{2}{8} = \dfrac{1}{4}\]
Therefore, time taken by Smith is
\[{T_1} = 15\min \]
Now let us calculate the total time taken to convey the message
= \[2hr\] (Jack started after this time) + \[3hr\] (Jack catches Smith in this time) + \[15\min \] (Smith meets Pamila in this time)
= \[2hr + 3hr + 15\min \]
= \[5hrs15\min \]
Therefore, Pamila get the message at \[5hrs15\min \] i.e., 5:15 O'clock

So, the correct answer is “Option A”.

Note: As we know the distance travelled is the total length of the path travelled between two positions at a certain time. Hence to find out the distance or total time taken by the person to travel is just combine all the time taken per hour then simplify the distance with respect to time.