Problem Setup

Let $t_c$ represent the time (in hours) Ravikant spent cycling.

Let $t_w$ represent the time (in hours) Ravikant spent walking.

The speed of cycling is $v_c = 12.5\text{ km/h}$.

The speed of walking is $v_w = 3\text{ km/h}$.

The total distance covered is $D = 40\text{ km}$.

The total time taken is $T = 7\text{ hours}$.

Equations Formulation

We can set up two main equations based on the given information:

1. Total Time Equation: The sum of cycling time and walking time equals the total time. $t_c + t_w = 7$
2. Total Distance Equation: The sum of the distance covered by cycling and walking equals the total distance. Distance = Speed $\times$ Time. $(v_c \times t_c) + (v_w \times t_w) = D$ Substituting the values: $(12.5 \times t_c) + (3 \times t_w) = 40$

Solving for Cycling Time ($t_c$)

We need to solve the system of two equations:

1. $t_c + t_w = 7$
2. $12.5 t_c + 3 t_w = 40$

From the first equation, express $t_w$ in terms of $t_c$: $t_w = 7 - t_c$

Substitute this expression for $t_w$ into the second equation:

Now, simplify and solve for $t_c$:

Combine the terms with $t_c$:

Subtract 21 from both sides:

Divide by 9.5 to find $t_c$:

Therefore, Ravikant spent 2 hours cycling.

Verification

If $t_c = 2$ hours:

• $t_w = 7 - 2 = 5$ hours.
• Distance cycled = $12.5 \text{ km/h} \times 2 \text{ h} = 25 \text{ km}$.
• Distance walked = $3 \text{ km/h} \times 5 \text{ h} = 15 \text{ km}$.
• Total distance = $25 \text{ km} + 15 \text{ km} = 40 \text{ km}$. (Matches the given total distance)
• Total time = $2 \text{ h} + 5 \text{ h} = 7 \text{ hours}$. (Matches the given total time)

The calculation is confirmed.