Question

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

Hint:

When speed changes by a fixed percentage, keep everything in terms of one speed (like \(w\)), express all distances using that speed and given times, then recompute the required times with the new speed.

Answer 1

Correct Answer: 444

Step 1: Define speeds.
Let Ankita's walking speed be \(w\) km/h. Her running speed is \(40%\) more: \[ r = 1.4w. \] Given: \[ 3 \text{ hours } 30 \text{ minutes} = 3.5 \text{ hours} = 210 \text{ minutes}. \] Step 2: Use the given times.
Walking from \(B \to C\): \[ \frac{\text{Distance } BC}{w} = 3.5 \Rightarrow \text{Distance } BC = 3.5w. \] Running from \(B \to A\): \[ \frac{\text{Distance } BA}{r} = 3.5 \Rightarrow \text{Distance } BA = 3.5r = 3.5(1.4w) = 4.9w. \] Step 3: Time to walk from A to B.
Walking from \(A \to B\), using speed \(w\): \[ \text{Time}(A \to B)_{\text{walk}} = \frac{\text{Distance } AB}{w} = \frac{4.9w}{w} = 4.9 \text{ hours}. \] Convert to minutes: \[ 4.9 \times 60 = 294 \text{ minutes}. \] Step 4: Time to run from B to C.
Running from \(B \to C\), using speed \(r = 1.4w\): \[ \text{Time}(B \to C)_{\text{run}} = \frac{\text{Distance } BC}{r} = \frac{3.5w}{1.4w} = \frac{3.5}{1.4} = 2.5 \text{ hours}. \] Convert to minutes: \[ 2.5 \times 60 = 150 \text{ minutes}. \] Step 5: Total required time.
\[ \text{Total time} = 294 + 150 = 444 \text{ minutes}. \]