Rakesh sets out to cycle from Delhi to Mathura and at the...

Rakesh sets out to cycle from Delhi to Mathura and at the same time Suresh starts from Mathura to Delhi. After passing each other they complete their journeys in 9 and 16 hours, respectively. At what speed does Suresh cycle if Rakesh cycles at $16 \mathrm{~km}$ per hour? (a) $12 \mathrm{~km} / \mathrm{hr}$ (b) $16 \mathrm{~km} / \mathrm{hr}$ (c) $14 \mathrm{~km} / \mathrm{hr}$ (d) None of these

Rakesh sets out to cycle from Delhi to Mathura and at the same time Suresh starts from Mathura to Delhi. After passing each other they complete their journeys in 9 and 16 hours, respectively. At what speed does Suresh cycle if Rakesh cycles at $16 \mathrm{~km}$ per hour?
(a) $12 \mathrm{~km} / \mathrm{hr}$
(b) $16 \mathrm{~km} / \mathrm{hr}$
(c) $14 \mathrm{~km} / \mathrm{hr}$
(d) None of these

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Uniform Motion

This concept refers to objects moving at a constant speed, where the relationship between distance, speed, and time is linear. Problems in uniform motion use the fundamental formula: distance equals speed multiplied by time. This principle is crucial for solving scenarios involving consistent travel rates, such as determining how far a person has gone over a span of hours.

Relative Speed in Opposing Directions

When two objects move towards each other, their speeds add up to give their relative speed. This concept is instrumental in meeting problems, where timing the meeting point depends on the sum of the speeds from both directions. Understanding relative speed helps in setting up equations that relate the distances covered by each object at the point they cross paths.

Ratio and Proportional Reasoning in Motion Problems

In many motion problems, the distances remaining after meeting points are inversely proportional to the speeds of the moving objects. This proportionality between time, distance, and speed allows one to compare different segments of the journey and solve for unknown speeds or distances by setting up proportional relationships. This method is key in problems where the time taken after meeting is used to deduce the unknown rate.

Transcript

Please give Ace some feedback