## Speed Time and Distance

Theory

The questions in this section can vary from being very easy to surprisingly difficult. This is a conceptual section and some of the questions can consume a lot of time. While solving, write down the equations as far as possible to avoid mistakes. The few extra seconds can help you avoid silly mistakes. Also, check if the units of distance, speed and time match up. So if you see yourself adding a unit of distance like m to a unit of speed m/s, you would realize you have missed a term. Choose to apply the concept of relative speed wherever possible as it can greatly reduce the complexity of the problem. Like speed and distance, in time and work while working with terms ensure that you convert all terms to consistent units like man-hours.

Tip

• In a journey travelled with different speeds, if the distance covered in each stage is constant, the average speed is the harmonic mean of the different speeds.
• In a journey travelled with different speeds, if the time travelled in each stage is constant, the average speed is the arithmetic mean of the different speeds.

Tip

While converting the speed in m/s to km/hr, multiply it by 3.6. It is because 1 m/s = 3.6 km/hr. Hence, 5 m/s = 5*3.6 km/hr = 18 km/hr

Formula

• Distance = Speed * Time
• Speed = Distance / Time
• Time = Distance / Speed

Formula

Time taken = Total Work / Speed of Doing work

Theory

When two or more people work together, we add their speed of doing work. So if A takes 6 days to do some work and B takes 3 days to do some work, their combined speed is 1/6+1/3 = 1/2. Hence, A and B together would take 2 days to do the same job.

Formula

If A and B are moving in opposite directions with speeds x m/s and y m/s respectively, their relative speeds with respect to each other will be
Relative Velocity = (x+y) m/s

If A and B are moving in the same direction with x m/s and y m/s then A’s relative velocity wrt B is
Relative Velocity = (x-y) m/s

and B’s relative velocity wrt A is
Relative Velocity = (y-x) m/s

Formula

If the speed of stream is 'W' and speed of a boat in still water is 'B'
• Speed of the boat downstream is B+W
• Speed of the boat upstream is B-W

Shortcuts

Two trains of length $$L_1$$ and $$L_2$$ travelling at speeds of $$S_1$$ and $$S_2$$ cross each other in
• $$\frac{L_1+L_2}{S_1+S_2}$$ if they are going in opposite directions
• $$\frac{L_1+L_2}{S_1-S_2}$$ if they are going in the same direction

Formula

• If X can do a work in 'n' days, the fraction of work X does in a day is $$\frac{1}{n}$$
• If X can do a work in 'x' days, and Y can do a work in 'y' days, the number of days taken by both of them together is $$\frac{x*y}{x+y}$$
• If $$A_1$$ men can do $$B_1$$ work in $$C_1$$ days and $$A_2$$ men can do $$B_2$$ work in $$C_2$$ days, then $$\frac{A_1 C_1}{B_1}$$ =$$\frac{A_2 C_2}{B_2}$$

Solved Example

Ram drove to a friend's place at 60 km/hr. He returned back at 50 km/hr but took 1 hour longer. What is the distance to his friend's place?

Explanation:
Let the distance be d km.
Time taken in first instance = d/60
Time taken in the second instance = d/50
d/50 = d/60+1
d = 300km

Solved Example

If 30 men can build a house in 30 days. How many men are needed to build the same house in 10 days?

Explanation:
We know the formula:
AB/C = ab/c
30*30/1 = 10*x/1
x = 90 days