Question

The distance between two points A and B is\[110km\]. A motorcyclist starts from A towards B at \[7am\] and at the speed of \[20km/hr\]. Another motorcyclist starts from B towards A at \[8am\] and at a speed of \[25km/hr\]. When will they cross each other?

Answer 1

Hint: In this question, we will apply the basic relation between distance-speed-time to calculate the required value. But, for the speed of one bike, we are going to use the formula of relative speed because the two are approaching each other.

Formula Used:
We are going to use the formula which describes the basic relation between distance-speed-time and is:
\[{\rm{Speed}} = \dfrac{{{\rm{Distance}}}}{{{\rm{Time}}}}\]

Complete step by step answer:

The above diagram defines the relation between the points and the bikes.
The given distance between A and B, \[d = 110km\]
The biker from the point A starts at time \[7am\],
so, when the clock hits at \[8am\], he traveled for time, \[t = 1hr\]
The speed of bike A \[{s_A} = 20km/hr\]
So, distance traveled by bike A in \[1hr\] = \[t \times {s_A} = 1 \times 20 = 20km\]
Remaining distance after \[1hr\] = \[110 - 20 = 90km\]
Now, when it is \[8am\], the biker from B starts.
So, the speed of bike B = their relative speed (because they are coming towards each other)
= \[20 + 25 = 45km/hr\]
So, the time taken = \[\dfrac{{{\rm{distance}}}}{{{\rm{relative\;speed}}}} = \dfrac{{90}}{{45}} = 2hr\]

Hence, they are going to cross each other after \[2hr\] from \[8am\], i.e., \[10am\].

Note: So, in questions like these, we need to remember the basic formulae and know how to apply them. Here, some students might wonder if we could apply the formula of relative speed to bike A instead of bike B, but we cannot as if we had applied that to bike A, then it would have meant that bike A is being driven under the influence of bike B starting from 7am, but that would have been factually wrong as bike B starts at 8am. Hence, it means that the relative speed formula can only be applied to bike B.