1. Speed, Time and Distance:

Speed = (Distance / TIme)

Time = (Distance / Speed)

Distance = (Speed * Time)

2. km/hr to m/sec conversion:

x km/hr = (x * 5/18) m/sec

3. m/sec to km/hr conversion:

x m/sec = (x * 18/5)km/hr

4. If the ratio of the speeds of A and B is a : b, then the ratio of the the times taken by then to cover the same distance is 1/a: 1/b or b: a

5. Suppose a man covers a certain distance at x km/hr and an equal distance at ykm/hr. Then,the average speed during the whole journey is [2xy/(x+y)]km/hr

### General Tips

Average speed= Total distance traveled/Total time taken

When the body travels at ‘u’ m/s for t1 seconds and ‘v’ m/s for t2 seconds, then
Average speed= (ut1+vt2)/(t1+t2).

There are other aspects of finding average speed
When the body travels ‘L’ distance at ‘u’ m/s and ‘M’ distance at ‘v’ m/s; Average speed = (Mu+Lv)/(L+M)

Stream: Moving water of the river is called stream.

Relative Speed: Speed of a moving body with respect to another moving body is called relative speed.

Speed of A with respect to B is as follows:-

When they are moving in same direction; Relative speed of A= A-B

When they are moving in opposite direction; Relative speed of A= A+B

Key points on Trains:

When a train is crossing a pole distance traveled by the train= length of train

When a train of length L is crossing a bridge of length B; the distance traveled by train=L+B

When a train of length L is crossing a platform of length P; then distance traveled by train=L+P

When a train of length L1 is crossing/ overtaking another train L2; then distance traveled = L1+ L2

Key points on Downstream/Upstream:

Definition: In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.

Still Water: If the water is not moving then it is called still water.

If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:

Speed downstream = (u + v) km/hr.

Speed upstream = (u – v) km/hr.

If the speed downstream is a km/hr and the speed upstream is b km/hr, then:

Speed in still water =(a+b)/2km/hr

Rate of stream=(a-b)/2 km/hr

Example 1

Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

Solution

Let the distance travelled by x km.

Let, (x/10)-(x/15)=2

3x - 2x = 60

x = 60 km.

Time taken to travel 60 km at 10 km/hr =(60/10)hours = 6 hours

So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.

Required speed =(60/5)kmph = 12 kmph