Quantitative Aptitude Time and Distance Study Material
The Speed of a body is the rate at which it is moving that is distance traveled in unit time. It is a measure by the distance, a moving body would cover in a given time. Thus, we see that the distance covered by a moving body depends on the speed of the body or person and the time taken.
(i) More distance, more time; at the same speed.
(ii) More speed; less time; for the same distance.
(iii) More speed; more distance in the same time.
(iv) If the speed of a body is changed in the ratio a : b then the ratio of time taken to cover a given distance changes in the ratio b : a.
Formulae: (i) Distance = Speed x Time
(ii) Speed = Distance/Time
(iii) Time = Distance/speed
Conversion of Units:
[Here, km = Kilometre; m = Metre; hr = Hour; S = Second]
Average Speed: If a certain distance is covered in parts at different speeds, the average speed is given by,
Average speed = Total distance covered/Total time taken
Velocity = The speed of a moving body is called its velocity if the direction of motion is also taken into consideration. Though, speed and velocity are interchangeably used in daily life, the two are different quantities. It is given by
Velocity = Net displacement of the body/Time taken
(a) Bodies moving in the same direction : (a) If two bodies move in the same direction, the relative speed of one with respect to the other is the difference of their speeds. For example, if the two cars A and B move in the same direc¬tion at speeds of 40 km/hr and 30 km/hr respectively, the relative speed of A with respect to B is (40 – 30) = 10 km/hr.
(ii) When two bodies move in the same direction, the distance between them increases/decreases at the rate of difference in their speeds. In other words, increase (or decrease) in distance between them after time t is equal to the product of difference in their speeds and time t.
Ex. 1. Two cars A and B start from the same point at speeds 40 km/hr and 30 km per hr respectively in the same direction. Find the distance between them after 3 hours.
Sol. Difference in speeds or Relative speed
= 40-30= 10 km/hr.
.’. Distance between A and B after 3 hours
= 10×3 = 30kmsAns
(b) Bodies moving in the opposite directions: (i) Relative speed of one with respect to the other is sum of their speeds.
(ii) Increase or decrease in distance between them equals product of their relative speed and time.
(iii) The distance between two bodies moving towards each other will get reduced at the rate of their relative speed (i.e., sum of their speeds). The time of their meeting (or crossing) is given by,
Meeting time = Initial distance between the two bodies/Sum of their speeds
Ex. 2. A person covers 800 metres in 160 seconds. Find his speed.
Sol. speed = Distance/Time = 800m/160s = 5 m/s
Ex. 3. A person runs at 5 km/hr. How much distance he will cover in 4 1/2 hours?
Sol. Time = 4 1/2 hrs = 9/2 hrs
Distance covered = Speed x Time
= 5*9/2 = 45/2 = 22(1/2) kms
Ex. 4. A person walks at 3 km/hr. In how much time he will cover 900 m?
Sol.: 3 km/hr= 3 x — m/s = — m/s 18 6
Time= 900/5/6-=1080 seconds. = 18 minutes Ans.
Note : During all calculations the respective units for distance, time and speed must be made consistent i.e, all distances must be expressed in the same unit, either metres or kilometres or yards as the case may be. Similarly, all time values must be expressed in the same unit, either hours, minutes or seconds.
Ex. 5. A person covers a distance d1 kms at s1 km/hr and then d2 kms at s2 km per hr. Find his average speed during the whole journey.
Ex. 6. A person leaves his house in the morning for office and returns to his house in the evening. In the morning he travels at a speed of 35 kms/hr but during return in the evening his speed is only 25 kms/hr. Find his average speed for the whole journey.
Sol. Here the two distances covered at two different speeds are equal i.e., d1 = d2.
Therefore, Average speed = 2x35x25/35+25
= 2x35x25/60 = 175/6 km/hr