In a 21 -meter race between a tortoise and a hare, the tortoise leaves 9 minutes before the hare

In a 21 -meter race between a tortoise and a hare, the...

Key Concepts

Race Strategy and Time Differences

Often in race problems, additional factors like head starts or time leads are introduced to account for the relative performance of competitors. Understanding how these time differences impact the effective time each participant has in a race, and incorporating them into the distance-rate-time equations, is vital for accurately modeling and solving the problem.

Distance-Rate-Time Relationship

This concept is based on the relationship distance = rate × time. It is a fundamental principle used in solving motion problems, enabling one to set up equations that relate the distance covered by an object to the rate at which it travels and the time taken. In race problems, this relationship is crucial for determining unknown quantities when two of the variables are provided or can be expressed in terms of each other.

System of Equations

In problems involving multiple moving objects with interrelated conditions, forming a system of equations is key. Each object’s motion can be modeled with its own distance-rate-time equation, and additional conditions—such as head starts or time differences at the finish—help create a set of linear equations. Solving the system allows one to find the values of unknown variables like speeds or times.

Unit Consistency and Conversion

Maintaining consistency in units is essential in any motion problem. When information is provided in different units (for example, time in minutes and speed in meters per hour), converting all quantities to compatible units ensures accuracy in the equations and the final solution.

Transcript

00:01 This is problem number 83 in which the question is based on the tortoise and hair race it is given that in 21 meter race between a tortoise and hair the tortoise leaves nine minutes before the hair the hair by running at an average speed of 0 .5 meter per hour faster than the tortoise okay no problem now we have to assume let the average speed of toys b v t and of here b v h so it is given that i'm burning in average speed per hour faster than the tortoise so we have v h equal to v h plus 0 .5 which means here is running at a speed at a speed 0 .5 meter second faster than the tortoise equation number one finish the line three minutes before the tortoise what are the average speeds okay so now uh we can say that the time taken by tortoise time taken by tortois to finish the race will be a distance by speed and the same for the hair will be 28 by vh.

01:57 Now we have something to ponder upon that time taken by tortoise will be 12 minutes more than time taken by the hair as three minutes.

02:11 It reaches starts nine minutes before and reaches three minutes, nine minutes before the tortoise leaves nine minutes before the hair and hair crosses the line three minutes before.

02:26 The tortoise so we can write here that the time taken time taken by the tortoise will be 9 plus 3 that is 12 minutes more than the hair now 12 minutes means everything is in meter per hour so we have is it in meter per hour meters per hour okay so we have to convert this in r so 12 minutes equal to 12 by 60 1 by 4 r sorry 1 by 5 r okay if we are right now the equation we will be finding out that 21 by 21 by we should say okay 21 by 201 by we should say okay 21 by that is time taken to complete the race by tortoise 21 by vh now we say that time taken by tortoise will be 12 minutes more than time taken by the hair so this is 1 by 5 hours more okay so 21 by now we have vh equal to vt plus 0 .5 so let us write vt 21 by vt plus 0 .5 1 by 5 okay so 21 by vt minus 21 by vt plus 0 .5 equal to 1 by 5 so 21 can be taken as common it will become 1 by vt minus 1 by vt plus 0 .5 equal to 1 by 5 okay, so let us divide both sides by 21 and solving this...

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