Ankita walks from A to C through B, and runs back through… | CAT 2025 Slot 3 QA Q17

CAT 2025 Slot 3QAArithmetic • Time, Speed & DistanceModerate

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

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Official Convenor Answer Key: 444

Verified Solution:

### Core Concept The problem involves calculating time taken for different distances at different speeds. The key formula used is:

\text{Time} = \frac{\text{Distance}}{\text{Speed}}

### Step-by-Step Solution

Define Variables:

Let walking speed be

v

Running speed is

1.4v

(40% more than walking speed).

Distance from A to B:

d_1

Distance from B to C:

d_2

Given Times:

Time to walk from B to C: 210 minutes.

Time to run from B to A: 210 minutes.

Calculate Distances:

Walking from B to C:

210 = \frac{d_2}{v}

⇒

d_2 = 210v

Running from B to A:

210 = \frac{d_1}{1.4v}

⇒

d_1 = 210 \times 1.4v = 294v

Calculate Required Times:

Walking from A to B:

\frac{d_1}{v} = \frac{294v}{v} = 294

minutes.

Running from B to C:

\frac{d_2}{1.4v} = \frac{210v}{1.4v} = 150

minutes.

Total Time:

294 + 150 = 444

minutes.

### 30-Second Shortcut Recognize that the time taken to cover each segment inversely relates to speed. Since running is 1.4 times faster, the time saved on the return trip can be calculated proportionally.

### Final Answer Correct Answer: 444

CAT 2025 Slot 3 QA Question 17

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CAT 2025 Slot 3 QA Question 17

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