Quick Review: Time, Speed & Distance

The most important relationship between these three quantities, and possibly the only one which needs to be known is,

Distance = Speed × Time

Speed = Distance traveled / Time

Time = Distance traveled / Speed

Average speed, if equal distances are covered at a km/hr and b km/hr is 2ab/a+b

If two bodies are moving in the same direction at a speed of a and b respectively, then their relative speed is the difference of the two speeds.

If two bodies are moving in the opposite directions at a speed of a and b respectively, then their relative speed is a + b.

Two objects A and B moving along a circular path in the same direction, having started simultaneously and from the same point traveling at speeds of a and b, will meet again when the faster object has gained one full circle over the slower object, i.e. when the relative speed |a-b|completes one full round. The two objects will again meet at the starting point at a time, which is the LCM of the time taken for each of the objects individually to complete one round.

If the length of a train is L meters and the speed of the train is S m/s, then the time taken by the train to pass a stationary man/pole is L/S sec.

If the length of the train is L₁ and its speed is S m/s and the length of a platform (stationary object of comparable length) is L₂, then the time taken by the train to cross the platform is (L₁ + L₂)/S sec.

If the lengths of 2 trains are L₁ (faster) and L₂ (slower) m, and their speeds are S₁ and S₂ m/s resp., then the time taken by the faster train to overtake the slower train is L₁+L₂/ S₁+S₂ sec, and the time taken for the trains to cross each other is L₁+L₂/ S₁+S₂ sec.

If the average speed of a train, without stoppages, is S₁ km/hr and the speed with stoppages is S₂, then Stoppage time (in min/hr) = S₁-S₂/S₁×60.

Problems about boats in stream: 

if the speed of the boat in still water is say B kmph and if the speed at which the stream is flowing is W kmph,

1. When the boat is traveling with the stream the speed of the boat = (B + W) kmph
2. When the boat is traveling against the stream the speed of the boat = (B – W) kmph.
3. If the upstream is denoted as U and downstream is denoted as D then
4. B = D+U/2,  W= D-U/2

Important Distance and Time Conversions:

• 1 km = 1000 meter
• 1 meter = 100 cm
• 1 hour = 60 min
• 1 min = 60 sec
• 1 hour = 3600 sec
• 1 km/hr = (1×1000/1×3600) = 5/18 m/sec.

If A beats B by x metres or s seconds, then the speed of B is x/s metres/sec.

If the length of a circular track is L m, and if A and B take x and y sec. respectively, to complete one round, then both of them will meet at the starting point after LCM (x, y) sec.

If the length of a circular track is L m, and if the speeds of A and B are x m/sec. and y m/sec respectively, then the time after which both of them will meet at a point other than the starting point is L/x-y sec, if they are running in the same direction and L/x+y, if running in the opposite direction.