Question

A bicyclist was going from point A to point B with a speed of 12 km/h. On the way back he increased his speed to 18 km/h and covered the distance in 15 minutes less. What is the distance between point A and point B?

Answer 1

The distance traveled by the certain object is the product of its speed and the time it traveled. Mathematically,

          D = st
where s is the speed,and t is the time. Substituting the known values,

      D = 12(x)

where x is the time in minutes. 
   
     D = 18(x - 15)

Equating the terms,

     12(x) = 18(x - 15)

The value of x from the equation is 45 minutes or 0.75 hour.

   D = (12 km/h)(0.75 h)
    D = 9 km

Answer: 9 km

Answer 2

Distance = Speed x Time. Let us denote distance as "D" and time as "T".
  So distance traveled by bicyclist while going from from point A to B is
 D = 12 x T (km/h)
 On the return journey the bicyclist increased his speed to 18 km/h and so reached 15 min less.
 15 minutes of 1 hour or 60 minutes is a quarter that is 1/4 or 0.25
 So distance traveled by bicyclist while returning is
D= 18 x (T- 0.25) km/h
 Lets Calculate T by equating both the equations
 12 T = 18 (T- 0.25)
 12T = 18T- 4.50
 12T-18T = - 4.50 -6
T = - 4.50
 T = 4.50/6 = 0.75 hrs
   Now lets calculate the distance by putting the time value in both equations D = 12 x 0.75 = 9 KM
 D = 18 x (0.75 - 0.25) = 9 KM