SOLUTION: Shivani walks from point A to B at 3 km/h and returns by bicycle at 12 km/h. Her return journey takes 2.5 hours less than her outward journey. Find her time for the entire jour

The rate bicycling is 4 times the rate walking.

Since the distance is the same, it means that the time walking is 4 times time bicycling.


So, if x is the time bicycling, then the time walking is 4x.


From the condition, you have this equation

    4x - x = 2.5 hours,

or

    3x = 2.5 hours


Hence, the time bicycling is  x =  hours.


It implies that the time for the entire two ways journey is

    x + 4x = 5x =  =  hours = 4 hours and 10 minutes.


ANSWER.  The entire journey takes  4 hours and 10 minutes.

Let time spent walking, be T

Then time spent riding = T - 2.5

We then get the following DISTANCE equation: 3T = 12(T - 2.5)

3T = 12T - 30

3T - 12T = - 30

9T = 30

Time spent walking, or 

Time spent cycling: 

Time taken to cover entire journey: