A lady travels a total distance of 3 km in 26 minutes. She walks at a speed of 6 km/hour for some distance and runs at 10 km/hour for the remaining distance. The problem asks us to find the distance she walks.

1. Problem Description

A lady travels a total distance of 3 km in 26 minutes. She walks at a speed of 6 km/hour for some distance and runs at 10 km/hour for the remaining distance. The problem asks us to find the distance she walks.

2. Solution Steps

Let $d_w$ be the distance she walks (in km), and $d_r$ be the distance she runs (in km).

Let $t_w$ be the time she spends walking (in hours), and $t_r$ be the time she spends running (in hours).

We know that the total distance is 3 km:

$d_w + d_r = 3$

We also know that the total time is 26 minutes, which is $\frac{26}{60}$ hours.

$t_w + t_r = \frac{26}{60} = \frac{13}{30}$

We know that distance = speed * time. Thus, time = distance / speed.

$t_w = \frac{d_w}{6}$

$t_r = \frac{d_r}{10}$

Substitute these expressions for $t_w$ and $t_r$ into the total time equation:

$\frac{d_w}{6} + \frac{d_r}{10} = \frac{13}{30}$

Multiply both sides of the equation by 30 to eliminate the fractions:

$5d_w + 3d_r = 13$

Now we have a system of two equations with two variables:

1. $d_w + d_r = 3$

2. $5d_w + 3d_r = 13$

From equation (1), we can express $d_r$ in terms of $d_w$:

$d_r = 3 - d_w$

Substitute this into equation (2):

$5d_w + 3(3 - d_w) = 13$

$5d_w + 9 - 3d_w = 13$

$2d_w = 13 - 9$

$2d_w = 4$

$d_w = \frac{4}{2} = 2$

Now, substitute the value of $d_w$ back into the equation for $d_r$:

$d_r = 3 - d_w = 3 - 2 = 1$

So, she walks 2 km and runs 1 km.

3. Final Answer

The distance she walks is 2 km.