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

Ankita moves from A to C via B and back again, with a walking speed and a running speed that is 40% faster. Let's define variables for clarity. Let the walking speed be w and the running speed be r where r = 1.4w due to the 40% increase. The distances between points are:

• d_AB: Distance from A to B
• d_BC: Distance from B to C

The time taken to walk from B to C, and run from B to A is equal: 3 hours 30 minutes.

Convert this to hours: 3.5 hours. Using the formula t = \(\frac{d}{s}\) (where t is time, d is distance, s is speed):

• Time to walk from B to C: \(\frac{d_{BC}}{w} = 3.5\)
• Time to run from B to A: \(\frac{d_{AB}}{1.4w} = 3.5\)

From these, derive the distances:

\(d_{BC} = 3.5w\) and \(d_{AB} = 4.9w\) (since \(\frac{3.5}{1.4} = 2.5\)).

The time Ankita takes to walk from A to B plus run from B to C is:

• Time from A to B: \(\frac{d_{AB}}{w} = 4.9\)
• Time from B to C: \(\frac{d_{BC}}{1.4w} = 2.5\)

Total time in hours: \(4.9 + 2.5 = 7.4\).

Convert hours to minutes: \(7.4 \times 60 = 444\) minutes.

Therefore, the total time is 444 minutes, fitting perfectly within the range 444,444 as specified.

Answer 2

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.
\[ \text{Total time} = 294 + 150 = 444 \text{ minutes}. \]