Important Formula: Speed, Distance and Time | Mathematics for RRB NTPC / ASM - RRB NTPC/ASM/CA/TA PDF Download

Speed

Speed can be defined as the rate at which an object covers distance in a specific direction within a given timeframe.

Distance

Distance can be defined as a scalar quantity that represents the numerical measure of the extent between two points in space.

Time

Time can be defined as the continuous and irreversible progression of events and existence and is typically measured in units like seconds(s), minutes(mins) and hours(hr).

Formulas of Train for Speed, Distance and Time

Train problems are very common problems which are asked in quantitative aptitude exams of companies, apart from basic speed distance and time questions hence students must focus on trains problems.

Here we have discussed some basic formulas required for train problems that are asked in exams

• Speed of the Train = Total Distance/Total Time Taken
• If  length of two trains is given, say t₁ and t₂, and the trains are moving in opposite directions with speeds of x₁ and y₁ respectively, then the time taken by trains to cross each other = T₁ + T₂ /X₁ + Y₁ 
• If the length of two trains is given, say t₁ and t₂, and they are moving in the same direction, with speeds x₁ and y₁ respectively, then the time is taken to cross each other = {(t₁+t₂) / (x₁-y₁)}
• When the start time of two trains is the same from position a and b towards each other and after crossing each other, they took t₁ and t₂ time in reaching  a and b respectively, then the ratio between the speed of  trains is = √T₂/√T₁ 
• If two trains leave station a and b at time t₁ and t₂ respectively and travel with speed X and Y respectively, then distanced from x, where two trains meet is = (T₂ − T₁) × (X × Y)/(X₁ - Y₁)
• The average speed of a train without any stoppage is x₁, and with the stoppage, it covers the same distance at an average speed of y₁, then Rest Time per hour = (Difference in average speed) / (Speed without stoppage)

Question and Answers on Speed Distance and Time

Q1: A high-speed train departs from City P to City Q at 8:00 AM. At the same time, another train leaves City Q and travels towards City P at a speed of 120 km/h. The distance between the two cities is 480 kilometers. If the high-speed train travels at a constant speed of 180 km/h, at what time will the two trains pass each other?
(a) 9 : 30 am 
(b) 4 : 30 am 
(c) 12 : 40 pm 
(d) 8 : 00 am
Ans: (d)
Sol: Let the time at which the two trains pass each other be T hours after 8:00 AM.
Distance covered by the high-speed train = 180 km/h * T hours Distance covered by the other train = 120 km/h * T hours
According to the problem, the total distance between the cities is 480 kilometers.
So, we can set up the equation: 180T + 120T = 480
300T = 480 T = 480 / 300 T = 1.6 hours
The two trains will pass each other 1.6 hours after 8:00 AM.

Q2: Arnold bane travels from one place to another at 60 km/hr and returns at 240 km/hr. If the total time taken is 5 hours, then find the Distance.
(a) 120 km
(b) 360 km
(c) 280 km
(d) 240 km
Ans: (d)
Sol: Here the Distance is constant, so the Time taken will be inversely proportional to the Speed. Ratio of Speed is given as 60:240, i.e. 1:4
So the ratio of Time taken will be 4:1. 
Total Time taken = 5 hours; Time taken while going is 4 hours and returning is 1 hour. 
Hence, Distance = 60x 4 = 240 km