This is a fairly straightforward question on the concept of Relative Speed.
Relative Speed is the speed of two objects that are moving simultaneously. In case of two objects that are moving in the same direction, the relative speed is the difference of the speeds.
If the objects are moving in opposite direction, the relative speed is the sum of the speeds.
But, the most important thing you need to remember is that you can calculate the relative speed only when both the objects are moving simultaneously.In this question, Devi and Mark both leave from Townsville and travel towards Villageton and are hence travelling in the same direction. Therefore, the relative speed will be the difference in their speeds.
However, the relative speed comes into effect only at 1:20 PM since Devi had been travelling alone between 1 PM and 1:20 PM.
20 minutes is 1/3rd of a hour; at 36 mph, distance travelled by Devi = 36 * \(\frac{1}{3}\) = 12 miles ( Distance = Speed * Time).
This means that, when Mark starts his journey, the distance between him and Devi is 12 miles. The relative speed = 51 – 36 = 15 mph. A schematic representation of this situation is shown below:
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29th Nov 2019 - Reply 3.jpg [ 26.47 KiB | Viewed 270 times ]
At this pace, time taken by Mark = \(\frac{12 }{ 15}\) = \(\frac{4}{5}\) hours = 48 minutes (Time = Distance / Speed)
Observe that we have taken Relative Speed in place of speed since both Mark and Devi are travelling simultaneously.
48 minutes from 1:20 PM would be 2:08 PM.
The correct answer option is E.
Note that the relative speed of 15 mph means that Mark gains 15 miles over Devi in every 1 hour; it can also mean that Devi loses 15 miles to Mark in every 1 hour. Therefore, to gain/lose 12 miles, it will take Mark/Devi, a time of 48 minutes.
Hope that helps!
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