Time and Distance :

i. Speed = Distance / Time

ii. Distance = Speed × Time

iii. Time = Distance / Speed

iv. Conversion of units :

One kilometer / hour = 1000 meter/60×60 Seconds = 5/18 m/sec.

∴ One meter/sec =18/5 km/hr.

1. Calculate the speed of a train which covers a distance of 300 km in 6 hours.

Solution : Speed = Distance covered/ time taken= 300/6= 50 km/hr.

2. How long does a train 100 meters long running at the rate of 60 km/hr take to cross a telegraphic pole?

Solution : In crossing the pole, the train must travel its own length.

∴ Distance travelled is 100 meters .

Speed = 60 km/hr. = 60×1000/60×60= 60000/3600

=16.66 sec.

3. A train running at a speed of 180 km/hr passes a pole on the platform in 20 sec. Find the length of the train in meters.

Solution : Speed of the train = 180 km/hr

= 180 × 5/18= 50 m/sec.

Length of the train = Speed of the train × time taken in crossing the pole

= 50×20=1000 meters

4. A ship sails to a certain city at the speed of 30 knots/hr and sails back to the same point at the rate of 60 knots/hr. What is the average speed of the whole journey?

Solution : Here, S1= 30 and S2= 60

∴ Average speed = 2× S1×S2/S1+S2= 2×30×60/30+60

= 3600/90=40 knots/hr.

5. A girl goes to school with the speed of 6 km/hr and returns with a speed of 4 km/hr. If she takes 10 hours in all, find the distance in km between the village and the school.

Solution : Here, S1= 6, S2=4 and T= 10

∴ The distance between the village and the school

= T(S1×S2/S1+S2) = 10(6×4/6+4) = 12 km.