CAT: Distance Time & Speed Test

A delivery van covers a total distance of 224 km in four stages, taking a total of 3 hours. The speeds of the van in the four stages are in arithmetic progression, and the times taken to complete the four stages are also in arithmetic progression. If the van travels at a speed of 960 meters per minute for 30 minutes during the first stage, then the distance, in meters, covered during the fourth stage is:

Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is

Two towns P and Q are 45 km apart and connected by a straight road. Rahul travels from P to Q while Karan travels from Q to P. They start at the same time and meet exactly 1 hour 30 minutes later. If Rahul reaches Q exactly 1 hour 15 minutes after Karan reaches P, what is Rahul's speed, in km per hour?

Two cyclists, Karan and Meera, start at the same time from opposite ends of a cycling trail and travel toward each other along the same route. After they meet, Karan takes 6 hours to reach Meera’s starting point, while Meera takes 24 hours to reach Karan’s starting point. If Karan cycles at a speed of 54 km/h, what is the total length, in km, of the cycling trail?

A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is

A tourist spent 8 hours travelling by train. Before the journey began, the train's total distance travelled was $x$ km, where $x$ is a whole number and is palindromic, i.e., $x$ remains unchanged when its digits are reversed. At the end of the journey, the train's total distance travelled was 26862 km, which is also palindromic. If the train never travelled at more than 110 km/h, then the greatest possible average speed during the journey, in km/h, was what?