Ankita walks from A to C through B, and runs back through the same route at a speed that is 40% more than her walking speed. She takes exactly 3 hours 30 minutes to walk from B to C as well as to run from B to A. The total time, in minutes, she would take to walk from A to B and run from B to C, is

The correct answer is 444.

Step-by-Step Explanation:

1. Understand the Speeds:

Let Ankita's walking speed be $v_w$.

Her running speed is 40% more than her walking speed. Therefore:

$v_r=1.4\⁢v_w=\frac{7}{5}{v}_w$

This means for any given distance, the time taken to run is $\frac{5}{7}$ of the time taken to walk that same distance, because speed and time are inversely proportional for a constant distance:

$t_{\text{run}}=\frac{5}{7}{t}_{\text{walk}}$

$t_{\text{walk}}=\frac{7}{5}{t}_{\text{run}}$

2. Analyze the Given Time Information:

We are given that she takes exactly 3 hours 30 minutes (which is 210 minutes) to walk from B to C as well as to run from B to A.

Let $W_{BC}$ be the time taken to walk from B to C, and ${\mathrm{Rpopular}}_{AB}$ (or $R_{BA}$) be the time taken to run from B to A.

$W_{BC}=210\text{minutes}$

$R_{AB}=210\text{minutes}$

3. Calculate Required Individual Times:

We need to find the total time, in minutes, to walk from A to B ($W_{AB}$) and run from B to C ($R_{BC}$).

Finding $W_{AB}$:

Since running from B to A takes 210 minutes, walking from A to B will take $\frac{7}{5}$ of that time:

$W_{AB}=\frac{7}{5}\⁢R_{AB}=\frac{7}{5}\⁢210=7\⁢42=294\text{minutes}$

Finding $R_{BC}$:

Since walking from B to C takes 210 minutes, running from B to C will take $\frac{5}{7}$ of that time:

$R_{BC}=\frac{5}{7}\⁢W_{BC}=\frac{5}{7}\⁢210=5\⁢30=150\text{minutes}$

4. Calculate the Total Required Time:

Total time to walk from A to B and run from B to C:

$\text{Total Time}=W_{AB}+R_{BC}=294+150=444\text{minutes}$