Question

I walked at 4 km/hr and missed the bus by 3 mins. However, if I walk at 5 km/hr, I reach the bus stand 3 mins early. How far is the bus stand from my home?

Answer 1

let in time t ,I reach the bus stand with a speed v m/min. and distance between home and bus stand is x meter(m).
4 km/hr = 4*1000/60 = 200/3 m/min
5 km/hr = 250/3 m/min
t = x/(200/3) - 3
t = x/(250/3) + 3
x/(200/3) - 3 = x/(250/3) + 3
x = 2000m
time = 2000/(200/3) - 3 = 27min.
speed = 2000/27 m/min
hence distance between bus stand and home = 2000m
I hope you will understand. if not understand please ask. 

Answer 2

Let the distance be x km
Case (i)
Speed = 4 km/hr
Reached time is 3 minutes delay to the original time (T)
Distance = speed * time
$x = 4(T + \frac{3}{60} )$
$x = 4(T + \frac{1}{20} )$
$x = 4T + \frac{1}{5}$       ......(1)

Case (ii)
Speed = 5 km/hr
Reached time 3 minutes before the scheduled time (T)
Distance = speed * time
$x = 5(T - \frac{3}{60} )$
$x = 5(T - \frac{1}{20} )$
$x = 5T - \frac{1}{4}$       ......(2)

Solving two equations, 

$4T + \frac{1}{5} = 5T - \frac{1}{4}$

$5T - 4T = \frac{1}{5} + \frac{1}{4}$

$T = \frac{9}{20}$

Substitute the value of T in any one of the equations

$x = 5( \frac{9}{20} ) + \frac{1}{4}$

$x = \frac{9}{4} + \frac{1}{4}$

$x = \frac{5}{2}$

The bus stand is  2.5 km from home