Two trains, one travelling 15 km/h faster than the other, leave the same station at the same time, one travelling east and other travelling west. At the end of 6 hours they are 570 km apart. What are the speeds of each train:

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40kmph and 55kmph

45kmph and 50kmph

40kmph and 55kmph

43kmph and 50kmph

answer is A.

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Detailed Solution

Let us assume that the speeds of train 1 and train 2 as V1,V2 respectively.
We are given that one travelling 15 km/h faster than other
Let us assume that train 2 is faster than train 1 then we get
⇒V2=V1+15........equation(i)
We are given that at the end of 6 hours they are 570 km apart
Let us assume that the distance between two trains as
⇒AB=570 km
Let us assume that the distance travelled by train 1 in 6 hours as OB
We know that the formula of speed is given as

speed = \frac{distance}{time}

By using the above formula we get the distance travelled by train 1 as
⇒V1=

\frac{OB}{6}

⇒OB=6V1
Let us assume that the distance travelled by train 1 in 6 hours as OA
⇒V2=

\frac{OA}{6}

⇒OA=6V2
From the figure we can say that the distance AB is divided into two parts as that is
⇒AB=OA+OB
Now, by substituting the required values in above equation we get
⇒570=6V2+6V1
⇒V1+V2=95
Now, let us substituting the value of V2 from equation (i) in above equation we get
⇒V1+V1+15=95
⇒2V1=80
⇒V1=40
By substituting this value in equation (i) we get
⇒V2=40+15
⇒V2=55
Therefore we can conclude that the speeds of two trains are 40kmph and 55kmph.

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