Time and distance

INTRODUCTION:
The problems based on time & distances are based on speed, time & distance. The general process to find out distance is as follows:
DISTANCE= SPEED*TIME.
where S is the speed of the moving object,
T is the time period & D is the distance covered.
Process to convert km/h in to m/s or vice versa is as follows:
1km/ h = 5/18 m/s
1 m/s = 18/5 km/h

Relative speed: The different between the speeds of two moving object with respect to their direction is known as relative speed. The relative speed according to the two different directions is as follows:
Case I: In case of same direction it is the difference between the speeds of the two moving objects.
Case II: In case of opposite direction it is the sum of the speeds of the two moving objects.

Example: Two objects are moving @ 30 km/h & 50 km/h. then the relative speed between them in two different cases are as follows:
Case I: In the same direction it is (50-30) i.e. 20 km/h
Case II: In case of opposite direction it is (50+30) i.e.80 km/h.

A boy goes to school @ 10 km/h & returns to his home @ 12 km/h respectively. If he takes 5 ½ hrs in all, find the distance between school & his home.

Solution

The L.C.M of two different speeds of 10 &12 is 60. If 60 km is the distance, then at the rate of two different speeds the times are 6 & 5 hrs respectively. When the total time is 6+5 i.e. 11hrs, the distance between the two points is 60 km. So when the total time is 5 ½ hrs, the distance between school & home is 30 km.

A person covers half of his journey @ 21 km/h, & the rest half @ 24 km/h respectively. If he takes 15 hrs in all, find the distance covered by the person.

Sol:
The L.C.M of 21 &24 i.e. 168. If 168 km is the distance, then the person covers ½ of it i.e. 84 km @ 21 km/h in 4 hrs and the rest half @ 24 km/h in 3 ½ hrs. So when the total time is 7 ½ hrs, the distance is 168 km. And if the total time is 15 hrs, the distance is 336 km.

A person goes a certain distance @ 48 km/h & returns to the starting point @ 96 km/h respectively. Find his average speed during the whole journey.

Sol:
The L.C.M of 48 @ 96 is 96.
If the distance is 96 km, then @ two different speeds the required time are 2 &1 hr respectively. Average speed= Total distance/Total time So the average speed i.e.(96+96)/2+1=64 km/h