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

Let the walking speed of Ankita be $$5x$$, implying that her running speed (which is $$40\%$$ more than her walking speed), is $$1.4\times 5x = 7x$$.

Thus, the ratio of her walking and running speeds is $$5:7$$. Therefore, the ratio of the time taken by Ankita to cover a fixed distance walking and running would by $$7:5$$.

She takes 3 hours 30 minutes, or $$3.5$$ hours to walk from B to C. Since Ankita is running from B to C in the second scenario, her time will reduce inversely to the ratio of her speed. The time taken by her to run from B to C would be $$\dfrac{3.5}{7}\times 5 = 2.5$$ hours.

She takes 3 hours 30 minutes, or $$3.5$$ hours to run from A to B. Since Ankita is walking from A to B in the second scenario, her time will increase inversely to the ratio of her speed. The time taken by her to walk from A to B would be $$\dfrac{3.5}{5}\times 7 = 4.9$$ hours.

Therefore, the total time it takes for Ankita in the second scenario is $$4.9+2.5 = 7.4$$ hours. This gives $$7.4*60 = 444$$ minutes.