Speed of a train is 30 percent more than the speed of a car. Both start from point P at the same time and reach point Q at the same time. P and Q are 130 km apart from each other. On the way train stops for 30 minutes at a station. What is the speed of the train?
Answer & explanation
Correct answer: option 1
Distance = Speed × Time
Let the speed of the car be x km/hr
According to the question, the Speed of a train is 40% more than the speed of a car. Therefore,
Speed of the train = x × \(\frac{140}{100}\) = \(\frac{7x}{5}\)
Time is taken by car to covered 280 km = \(\frac{280}{x}\)
Since the train stops for 60 minutes, i.e. 1 hr.
Time is taken by Train = \(\frac{280 × 5}{7x}\) + 1
Since, both time are equal, then
\(\frac{1400}{7x}\) + 1 = \(\frac{280}{x}\)
\(\frac{200}{x}\) + 1 = \(\frac{280}{x}\)
200 + x = 280
x = 80 km/hr
Speed of train = \(\frac{7x}{5}\) = \(\frac{7 × 80 }{5}\ = 112 km/hr