Time and Distance - Important Points
Time and distance is one of the important topics of Quantitative Aptitude. There are variety of questions in time, speed and distance. Here, we are covering important points and formula on time and speed general questions, average speed and relative speed.
Speed: Speed is the rate at which distance is covered i.e. S = D/T and thus unit of speed is km/h or m/s.
Time and Distance formula
Speed = Distance/Time OR Time = Distance/Speed OR Distance = Speed x Time
1km/hr = 5/18 m/s
1 m/s = 18/5 Km/hr
Proportionality relation between Time, Speed and Distance
Speed is directly proportional to distance when time is constant, means when speed increases distance increases, when speed decreases distance decreases if time is constant.
S1/S2 =D1/D2
Speed is inversely proportional to time if distance is constant, that is if speed increases time will be less but if speed decreases it will take more time if distance is constant.
S1/S2 =T2/T1
If the ratio of the speed of A and B is SA : SB, then the ratio of the time taken by them to cover the same distance is 1/SA : 1/SB or SB : SA
Average Speed
Average speed is defined as the total distance travelled divided by the total time taken to travel the same distance.
Average speed = Total distance travelled / Total time taken
Suppose A travels D1 km with S1 speed, D2 km with S2 speed, and D3 km with S3 speed then,
Average speed = (D1+D2+D3) / (D1/S1 + D2/S2 + D3/S3)
Average Speed Formula
Forward and Return Journey: Suppose a man covers a distance at x km/h and an equal distance(returns back) at y km/h, then-
Average speed during the whole journey = (2xy / x+y) km/h
If 3 equal distance is covered with 3 different speeds x, y and z –
Average Speed = 3 (xyz)/(xy + yz + xz)
viii) An object that moves at a constant rate is said to be in uniform motion. The formula d= rt gives the relationship between distance d, rate r, and time t. Uniform motion problems may involve objects going the same direction, opposite directions, or round trips.
Example1:A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be.
Solution: Time = 50/60 hr = 5/6hr
Speed = 48mph
distance = S*T = 48 * 5/6 = 40km
time = 40/60hr = 2/3hr
New speed = 40* 3/2 kmph = 60kmph
Relative Speed
If two bodies are moving (in the same direction or in the opposite direction), then the speed of one body with respect to the other is known as its relative speed.
Relative speed is a phenomenon that we observe in our daily life. Suppose you are travelling in a car and there is another car coming from the opposite direction, then it seems that the other car is moving much faster than actual. This is the case when objects are moving in opposite direction.
If both the cars are moving in the same direction then the passenger of slower car observes that the faster car is moving slowly than its actual speed. And if both the cars are moving at the same speed, then, they seem to be stationary if seen from one of the cars, even though they might actually be at a speed of 100 km/hr each.
Relative Speed Formula
Formula for relative speed depends on the case whether objects are moving in same direction or opposite direction.
When objects moving in same direction
Relative Speed = S1 – S2 (S1 > S2)
When objects moving in opposite direction
Relative Speed = S1 + S2
Time to overtake faster vehicle to slower one = Relative Distance/(S1 – S2)