Speed, Time and Distance topic is quite common in most of the important competitive exams. But this entire topic revolves around one simple concept, viz. ‘the distance travelled/covered by a person/object is directly proportional to the speed of the journey and to the amount of time taken’.
In other words, Distance covered = Speed * Time
This same formula can be rewritten as:
Speed = Distance travelled /Time taken
Alternatively, it can also be written as:
Time taken = Distance covered/Speed
These three formulae would enable you to answer every problem in this topic
Note : If you multiply speed given in km/hr with 5/18, it will give you the speed in m/s. Similarly, if you divide speed in m/s with 5/18 (i.e. multiply it with 18/5), it will give you the speed in km/hr. Remember this simple trick always.
For example : 400 km/hr * (5/18) = 111.11 m/s
If distance covered is constant, the ratio of time taken would be inversely proportional to speed.
Thus, S1/S2 = T2/T1 or S1:S2 = T2:T1 (when distance covered is constant
Let’s try an example to understand this better.
While travelling by road to his office and back, Tarun noticed that the ratio of time taken to and fro was 4:7. He also noted that his speed in the evening was 48 km/hr. Can you calculate Tarun’s speed in the morning?
As we know that, when distance covered is constant, time is inversely proportional to speed.
Hence, T1:T2 = 4:7 = S2:S1
Thus, 48:S1 = 4:7
S1 = 48 * 7/4 = 12 * 7 = 84 km/hr
Also note another very similar relation – If time taken for two journeys is constant, then the distance covered would be proportional to the speed of the journey.
Let’s understand this through an example.
Luke, a space traveler, reached his father’s office on an inter-galactic bus after a 4 hour journey. He then took his dad’s Galaxy Crosser supercar and reached his mother’s place in 4 hours. But, he noticed that the ratio of speeds over the two journeys was 3:7. If the Galaxy Crosser has a speed of 63,000 km/hr, Calculate the total distance that Luke covered over the two journeys.
Since the time taken in both journeys is the same, the distance covered in the two journeys would be directly proportional to the speed during the two journeys.
Hence, Ratio of speed S1:S2 = 3:7 = D1:D2
We know that S2 = 63,000 km/hr and S1/S2 = 3/7
Thus, S1 = 63,000 * 3/7 = 27,000 km/hr
As he travelled for 4 hours both times, the total distance covered is
D1 + D2 = 27,000*4 + 63,000*4
= 108,000 + 252,000 = 360,000 km