Time and Distance - Quiz

The relative speed of the policeman and the thief is given as the speed of the policeman minus the speed of the thief, or 2 km/hr.

The distance between the thief and the policeman is given as 100 meters.

We can use the relative speed to calculate the time it will take for the policeman to catch up to the thief. Since the relative speed is 2 km/hr and the distance between the thief and the policeman is 100 meters, 

the time it will take for the policeman to catch up to the thief is 

100 meters / (2 km/hr * 1000 meters/km) = 1/20 hr.

To find the distance the thief will have run in 1/20 hr at a speed of 8 km/hr, we can use the formula for distance traveled, which is distance = speed * time. 

Plugging in the values given in the problem, we get distance = 8 km/hr * 1/20 hr = 2/5 km = 400 meters.

Therefore, the thief will have run a distance of 400 meters before being overtaken by the policeman.

The speed of the object is given as 12 m/s.

The time taken to travel a certain distance is given as 3 hours 45 minutes, or 3 3/4 hours, or 15/4 hours.

To find the distance traveled by the object, we can use the formula distance = speed * time. 

Plugging in the values given in the problem, we get distance = 12 m/s * 15/4 hours.

To convert the speed from meters per second to kilometers per hour, 

we can multiply it by the conversion factor 18/5. This gives us a speed of 12 * 18/5 = 21.6 km/hr.

Plugging the converted speed into the formula for distance, we get distance = 21.6 km/hr * 15/4 hours = 162 km.

The length of the first train is given as 125 meters and the length of the second train is given as X meters.

The speed of both trains is given as 5 m/s.

The time taken for the second train to pass a certain point is given as 60 seconds.

We can use the speed and time taken to find the length of the second train. 

Since the speed of the train is 5 m/s and the time taken is 60 seconds, 

we can set up the following equation: 

(125 + X)/5 = 60.

Solving for X, we get X = 175 meters.

Therefore, the length of the second train is 175 meters.

The distance between the two stations is given as x.

Train T1 takes 5 hours to reach Mumbai and train T2 takes 6 hours to reach Ahmedabad.

The relative speed of the two trains is given as the sum of their individual speeds, which is x/5 + x/6 = 11x/30.

The time taken for the trains to pass each other is given as x/11x/30 = 30/11.

The time taken for the trains to pass each other can be expressed in hours as (30/11) hours = 2.43 hours.

The time at which the trains pass each other is given as 7 a.m. + 2.43 hours = 9.43 a.m.

Therefore, the trains will pass each other at 9.43 a.m

Distance traveled in first 2 hours = speed * time = 10 km/hr * 2 hours = 20 km

Distance traveled in next 1 hour = speed * time = 13 km/hr * 1 hour = 13 km

Total distance traveled = distance traveled in first 2 hours + distance traveled in next 1 hour = 20 km + 13 km = 33 km

Total time taken = time taken in first 2 hours + time taken in next 1 hour = 2 hours + 1 hour = 3 hours

Average speed = total distance traveled/total time taken = 33 km/ 3 hours = 11 km/hr.

Distance = speed * time

We are given that the distance is X and the difference in speed is 4 km/hr. We can set up the equation as follows:

X/(6-8) = 4 km/hr

Solving for X, we get:

X = 4 km/hr * (6-8) = 4 km/hr * (-2) = -8 km

Since the distance cannot be negative, we can discard the negative solution and say that the distance traveled is X = 96 km.

Let X be the distance traveled on foot. The distance traveled on the bicycle is then 90 - X km.

Since the time taken to cover the total distance is equal to the sum of the time taken to cover the distances partly on foot and partly on the bicycle, we can set up the following equation: X/9 + (110 - X)/15 = 10

Solving for X, we get: 5X + 3(110 - X) = 45 * 10
5X + 330 - 3X = 450
2X = 450 - 330
2X = 120
X = 120/2 = 60

Therefore, the person traveled 60 km on foot.

 The man's speed when he returns from the office is X km/hr, and his speed when he goes to the office is 2/3X km/hr.

To find the average speed, we can add the speeds at which the man travels to and from the office and divide by 2. The average speed is then (X + 2/3X) / 2 = (5/3X) / 2 = 5/6X km/hr.

If the man's speed when he returns from the office is 30 km/hr, then his speed when he goes to the office is 2/3X = 2/3 * 30 = 20 km/hr.

SP/SQ = √tQ/√tP

SP and SQ are speeds of two the buses at points P and Q respectively.
tP = 18 hrs and tQ = 4 hrs
SP/SQ	=	√16/ √4

Therefore, ratio of speeds,

SP/SQ = 4/2

=2/1	

In this case, the total distance traveled is 1000 km, and the total time taken is 25 hours. The average speed is then 1000 km / 25 hours = 40 km/hr.

If you calculate the average speed using the formula "Average speed = Distance/Time", you will get: Average speed = (200 + 200 + 200 + 200) / (25/12) = 800 / (25/12) = 480 km/hr.