Profile
Settings
Refer your friends
Sign out
Distance Between Speeds Time is one of the most popular and crucial topics in any competitive exam’s Mathematics or Quants portion. The concepts of speed, time, and distance are frequently utilized in issues about motion in a straight line, circular motion, boats and streams, races, and clocks, among other things. Aspirants should endeavour to comprehend how the components of speed, distance, and time interact.
The Speed, Time, and Distance Relationship:
- Distance/Time = Speed — This informs us how fast or slow an object moves.
- Distance is directly proportional to speed, but time is inversely proportional to speed.
- Distance is equal to the product of speed and time, and
- Time equals distance divided by speed; as speed increases, the time taken decreases, and vice versa.
However, when utilising formulas, it’s also crucial to remember to use the right units.
Speed Measurement Units Distance & Time
Different units can be used to indicate speed, distance, and time:
Time is measured in unit of seconds (s), minutes (min), and hours (h) (hr)
(Metres (m), kilometres (km), miles (miles), and feet(ft)
m/s and km/hr are units of measurement for speed.
So, if the Distance = km and the Time taken = hr, Speed = Distance/ Time, and Speed units are km/ hr.
The use of speed, time, and distance
A few subheads underneath the Speed, Time, and Distance themes are listed below, and they explain the basis for the various types of questions answered in the exam.
AVERAGE SPEED:
(Total distance travelled)/Average Speed = (Total time taken)
Case 1: Whenever the distance is constant: Average speed = 2xy/x+y; where x and y are the two speeds used to traverse the same distance.
Case 2: Average speed = (x + y)/2; where x and y are the two speeds at which we travelled for the same amount of time.
2. Speed & Time Inverse Proportionality:
When the distance is constant, speed will be inversely proportional to time. When D is constant, S is inversely proportional to T. The time taken will be in the ratio n:m if the speeds are in the ratio m: n.
There are two approaches to answering questions:
- Inverse Proportionality is a method of estimating the size of a group.
- Making Use of the Constant Product Rule
Example 1: After going 50 kilometres, a train is involved in an accident & travels at a third of its normal speed, arriving 45 minutes late. If the accident had occurred 10 kilometres further on, the delay would have been 35 minutes. Where can I find the typical Speed?
Using the Inverse Proportionality Method as a Solution
There are two scenarios here.
Case 1: an accident occurs at a speed of 50 km/h.
Case 2: an accident occurs at a speed of 60 km/h.
The difference between the two scenarios is merely 10 kilometres between 50 and 60 kilometres. The ten-minute timing differential is attributed only to these ten kilometres.
3. Meeting Point Questions
If two people go from point A and Point B in the same direction and meet at point P, they are said to be travelling in the same direction. They will cover AB in total distance during the meeting. Both of them will take the same amount of time to meet. Because Time is constant, the distances AP & BP will be proportional to their Speed. Let’s say A and B are separated by d.
When two persons walk from point A to point B towards one another for the first time, they traverse a distance “d” together. They traverse a “3d” distance together when they meet for the second time. They cover a distance together when they meet for the third time.
Example 1: Amit and Aman had to drive their separate automobiles from Delhi to Jaipur. Amit is driving at 60 kilometres per hour, while Aman is travelling at 90 kilometres per hour. Calculate how long it will take Aman to get to Jaipur if Amit takes 9 hours.
Solutions: The Time required will be inversely proportional to the Speed in both circumstances since the Distance covered is constant in both. The ratio between Amit’s and Aman’s speeds in the problem is 60:90 or 2:3.
As a result, the ratio of time consumed by Amit to time taken by Aman will be 3:2. Aman will take 6 hours if Amit takes 9 hours.
Conclusion
First, double-check that you understand the formula triangle. The key to answering that question is to know the formula completely and out so you always know which equation to apply, regardless of whether the exam question asks you to calculate speed or distance.
You will save time while answering questions if you make sure you have memorised the formula in all of its forms.
Second, you should concentrate on honing your overall math skills. You might be given a compound issue, which requires you to apply the formula in combination with other math abilities to solve the problem.
