Question

A and B start from a given point and travel on a straight road with average speeds of 30 km and 50 km
hour. A starts at 9 a.m. and B starts 3 hours later. Find the time when B meets A. Find also the
distances travelled by them before they meet.


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Answer 1

Answer:

I am not going to solve the problem for you. Rather I will make you clear about the concept and approach behind it.

Okay so it's given that the average velocities of A and B are 30Kmph and 50Kmph respectively.

Therefore the first step is to write down,

Va = 30Kmph

Vb = 50Kmph

Perfect. Now let's imagine the situation that's given, on which we have to analyse and find the solution of it.

At time t=0, the vehicle A started its journey with an average velocity Va = 30Kmph. So after 3 hours it has reached a point X. At that time another vehicle B will start it's journey.

So it's given that the two vehicles are going to meet up at another point say Y and we have to find the distance that was required by both of them to travel to get into such a situation.

From the paragraph in italics, we can inturn see that Vehicle B is lagging behind Vehicle A by a duration of 3 hours. So, at a particular time t = T, the two vehicles A and B are going to meet together for the first time in its journey. So at that point the distance traced by each of them are going to be the same but the time traveled by each are going to differ by 3 hours.

Let t = t1 be the time required by Vehicle A to reach Y and t = t2 be that required by Vehicle B

So,

t1 - t2 = 3

Va x t1 = Vb x t2

( Distance traced by each are equal)

Therefore solving both of them you will obviously get the answer and then from that you will be able obtain the distance from the simple Velocity - Time relation in rectilinear motion.

The answer would come out to be as such

t1 = 7.5 hours

t2 = 4.5 hours

D = 225 Kilometres.

PS -

Here the average velocity of the vehicles are given. So it would be reasonable to assume that the vehicles are traveling with a uniform velocity of 30 and 50Kmph respectively without any acceleration. Thus the formula VxT.