Two cars are moving in the same direction with a speed of 45 km/hr and a distance of 10 km separates them. If a car coming from the opposite direction meets these two cars at an interval of 6 minutes, its speed would be
[amp_mcq option1=”45 km/hr” option2=”55 km/hr” option3=”65 km/hr” option4=”75 km/hr” correct=”option2″]
This question was previously asked in
UPSC CAPF – 2013
Let the speed of the car coming from the opposite direction be V km/hr. The two cars moving in the same direction have a speed of 45 km/hr and are separated by a distance of 10 km. The relative speed of the oncoming car with respect to either of the cars is (V + 45) km/hr, since they are moving in opposite directions. The oncoming car meets the two cars at an interval of 6 minutes. This means that the time taken by the oncoming car to cover the distance of 10 km that separated the two cars, relative to one of the cars, is 6 minutes. 6 minutes = 6/60 hours = 1/10 hours.
Using the formula: Distance = Relative Speed × Time
10 km = (V + 45) km/hr × (1/10) hr
10 = (V + 45) / 10
10 × 10 = V + 45
100 = V + 45
V = 100 – 45
V = 55 km/hr.
The speed of the car coming from the opposite direction is 55 km/hr.
When two objects move in opposite directions, their relative speed is the sum of their individual speeds. Distance = Speed × Time.