 ## Time, Distance and Work

Theory

The questions in this section can vary from being very easy to surprisingly difficult. This is a conceptual section (especially questions involving clocks) 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.
Formula
• If the speed of water is 'W' and speed of a boat in still water is 'B'

1. Speed of the boat downstream is B+W
2. Speed of the boat upstream is B-W
Formula
• 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 $$\frac{A_1 C_1}{B_1}$$ =$$\frac{A_2 C_2}{B_2}$$
Formula
• 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
Tip
• In a well functioning clock, both the hands meet after every $$\frac{720}{11}$$ mins. It is because relative speed of minute hand with respect to hour hand = $$\frac{11}{2}$$ degrees per minute.