Formulas To Solve Time & Distance Problems

1). Speed, v = s/t. where s = Total distance, t = Total time
2). The relative velocity of two bodies moving at velocities u and v (u>v) in the same direction is (u – v).
3). The relative velocity of two bodies moving in opposite directions is (u + v).
4). A train or a moving body of known length has to travel its own length in passing a lamp post or a fixed body of insignificant size.
5). A train or a moving body must travel its own length plus the length of the stationary body in question, if the train or the moving body has to pass a stationary body i.e. a bridge, a railway platform etc.
6). Motion downstream or upstream:
Velocity of boat downstream = (u + v)
Velocity of boat upstream = (u – v)
Where ‘u’ is the velocity of the boat in still waters and ‘v’ is the
velocity of the stream.
7). If a man changes his speed in the ratio u : v, the corresponding ratio of times will be v : u

### FORMULAS FOR Time & Work PROBLEM ###

1. If a person can do a piece of work in ‘m’ days, he can do 1/m of the work in 1 day.

2. If the number of persons engaged to do a piece of work be increased (or decreased) in a certain ratio the time required to do the same work will be decreased (or increased) in the same ratio.

3. If A is twice as good a workman as B, then A will take half the time taken by B to do a certain piece of work.

4. Time and work are always in direct proportion.

5. If two taps or pipes P and Q take ‘m’ and ‘n’ hours respectively to fill a tank, then the two pipes together fill (1/m + 1/n) part of the tank in 1 hour and the entire tank is filled in mn/(m+n) hours.