A lady travels a total distance of 3 km by walking and running. She walks at a speed of 6 km/hour and runs at a speed of 10 km/hour. The total time taken is 26 minutes. The problem asks to find the distance she walked.

1. Problem Description

A lady travels a total distance of 3 km by walking and running. She walks at a speed of 6 km/hour and runs at a speed of 10 km/hour. The total time taken is 26 minutes. The problem asks to find the distance she walked.

2. Solution Steps

Let $d_w$ be the distance walked (in km) and $d_r$ be the distance run (in km).

Let $t_w$ be the time spent walking (in hours) and $t_r$ be the time spent running (in hours).

We know that the total distance is 3 km, so

$d_w + d_r = 3$ (Equation 1)

The total time taken is 26 minutes, which is $\frac{26}{60} = \frac{13}{30}$ hours. So,

$t_w + t_r = \frac{13}{30}$ (Equation 2)

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

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

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

Substitute these into Equation 2:

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

Multiply both sides by 30 to eliminate fractions:

$5d_w + 3d_r = 13$ (Equation 3)

From Equation 1, we can write $d_r = 3 - d_w$. Substitute this into Equation 3:

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

$5d_w + 9 - 3d_w = 13$

$2d_w = 13 - 9$

$2d_w = 4$

$d_w = 2$

Therefore, the distance she walked is 2 km.

3. Final Answer

2 km