Two people drive towards each other from two places which are $ 56 ext{ km}$ apart. The speed of the first pe

Question

Two people drive towards each other from two places which are $ 56	ext{ km}$ apart. The speed of the first person is $ 13	ext{ km/h}$ and speed of the other is $ 14	ext{ km/h}$. After how long will they be $ 2	ext{ km}$ apart if they start driving together?

Examoogle · Accepted Answer

The correct answer is Option A: 2 hours. Calculate relative speed ($13 + 14 = 27$ km/h). Subtract the target distance from total distance ($56 - 2 = 54$ km) and divide by relative speed ($54 / 27 = 2$ hours).

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate relative speed ($13 + 14 = 27$ km/h). Subtract the target distance from total distance ($56 - 2 = 54$ km) and divide by relative speed ($54 / 27 = 2$ hours).

Formula Used: $$t = \frac{D_{initial} - D_{final}}{v_1 + v_2}$$

Given: Distance between two places = 56 km. Speed of first person = 13 km/h. Speed of second person = 14 km/h. Target remaining distance = 2 km.

Steps: Calculate Relative Speed: Since the two people are driving towards each other, their relative speed is the sum of their individual speeds.. Calculate Effective Distance to Cover: They need to be 2 km apart, so they must cover the difference between the total distance and the target distance.. Calculate Time: Using the time formula $t = \frac{D}{v}$, substitute the effective distance and relative speed.

Answer: A is correct because the two people will be 2 km apart after covering a combined distance of 54 km at a relative speed of 27 km/h, resulting in 2 hours.

Exam Tip: This concept of relative speed is crucial for train-crossing problems and boat-stream problems in competitive exams.

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)