# Time & Distance

1. Speed, Time and Distance:

Distance = (Speed Ã— Time).
2. km/hr to m/sec conversion:

x km/hr =  m/sec.
3. m/sec to km/hr conversion:

x m/sec =  km/hr.

If the ratio of the speeds of A and B is a : b, then the ratio of the the times taken by than to cover the same distance is  or b : a.
4. Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then, the average speed during the whole journey is km/hr.

# Concept Related to Trains

1. Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.
2. Time taken by a train of length l metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres.
3. Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u - v) m/s.
4. Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.
5. If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then: The time taken by the trains to cross each other = .
6. If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then: The time taken by the faster train to cross the slower train = .
7. If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:

(A's speed) : (B's speed) = (b : a)

# Boats & Streams

1. Downstream/Upstream:

In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.
2. 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.
3. If the speed downstream is a km/hr and the speed upstream is b km/hr, then:

Speed in still water = (a + b) km/hr.

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