Question

A fast train takes 3 hours less than a slow train travelling 600 km. If the speed of a slow train is 10 km/hr less than the speed of a fast train, find the speed of both the trains.

Answer 1

Hint: In this particular type of question we need to express the speed of both the trains as x and x + 10 and use it to find the time taken by both of the trains to cover 600 km. Then we have to use the information given in the question to generate the quadratic equation and find the speed of both the trains.

Complete step-by-step answer:
Let the speed of the slow train be x km/h.
And the speed of the fast train is (x + 10) km/h.
Time taken by slow train to cover 600 km = $\dfrac{{600}}{x}$hrs (since time=$\dfrac{{{\text{distance}}}}{{{\text{speed}}}} $ )
Time taken by fast train to cover 600 km = $\dfrac{{600}}{{x + 10}}$hrs
According to the question, the fast train takes 3 hours less than the slow train travelling 600km.
$
   \Rightarrow \dfrac{{600}}{{x + 10}} + 3 = \dfrac{{600}}{x} \\
   \Rightarrow \dfrac{{600 + 3x + 30}}{{x + 10}} = \dfrac{{600}}{x} \\
   \Rightarrow 630x + 3{x^2} = 600x + 6000 \\
     \Rightarrow {x^2} + 10x - 2000 = 0 \\
   \Rightarrow {x^2} + 50x - 40x - 2000 = 0{\text{ }}\left( {{\text{splitting the middle term}}} \right) \\
   \Rightarrow x\left( {x + 50} \right) - 40\left( {x + 50} \right) = 0{\text{ }} \\
   \Rightarrow \left( {x - 40} \right)\left( {x + 50} \right) = 0 \\
   \Rightarrow x = 40, - 50 \\
$
Since speed can’t be negative
x = 40km/hr
Speed of slow train = x = 40 km/h
Speed of fast train = x + 10 = 40 + 10 = 50 km/h.

Note: Remember to recall the formula of speed to be used in this type of question. The negative value of x is not considered as the speed of the train cannot be negative. Note that we can also consider x as the speed of the faster train as it won't affect our final answer.