# Math Book 2: Races

Rates, Speed Time distance

Races is an extension of speed time distance. You could expect one question in the GMAT quant section testing ideas covered in this chapter. This topic tests the idea of people racing against each other, racing with a head start, dead finish and other related ideas.

### Concepts Covered

The chapter on Races is essentially an extention to the concepts covered in the Speed Time and Distance Chapter and Ratio Proportion chapter. The lesson book has questions on two types of races - Races along a straight track and Circular Races. Wizako's GMAT Math Lesson Book in this chapter covers the following concepts:

1. Definition of the term race
2. Explanation of the concept of races along a straight track
3. Illustrative Examples to consolidate the idea
4. 8 solved examples are provided with detailed explanation for races along a straight track
5. The concept of race in a circular path is explained along with examples
6. 4 solved examples are given with detailed explanation
7. 13 exercise problem of both types of races with the answer key and explanatory answers
8. A multiple choice test with 26 GMAT level questions. Explanatory answers to all questions and an answer key are provided for the test.

Here is a typical solved example from this chapter.

### Sample Question

P and Q run around a circular track of radius 49 meters starting from the same point at the same time and in the same direction. If 'P' runs at a speed of 15 m/min and 'Q' runs at a speed of 10 m/min, when will they meet again for the first time?

P and Q run in the same direction. Therefore, their relative speed = 15 - 10 = 5 m/min

Circumference of the circular track is the length of the circular track = 2$$pi$r = 2 * $\frac{22}{7}$ * 49 = 308 m. Time taken for P and Q to meet for the first time after they have started a race along a circular track, starting simultaneously from the same point is $\frac{\text{length of the circular track}}{\text{relative speed}}$ = $\frac{308}{5}$ = 61.6 minutes 61.6 minutes =$60 + 1 + 0.6) minutes = 1 hour, 1 minute and (0.6 * 60) seconds

Therefore, they will meet for the first time after 1 hour, 1 minute and 36 seconds.

### Chapterwise details of Wizako's Math Lesson Books

Math Lesson Book 1

 1 Linear Equations Details 2 Quadratic Equations Details 3 Set Theory Details 4 Sequences & Series Details 5 Number Properties & Theory Details 6 Inequalities Details 7 Functions

Math Lesson Book 2

 1 Descriptive Statistics Details 2 Ratio Proportion Details 3 Mixtures 4 Interest 5 Rates: Speed Distance Details 6 Rates: Races Details 7 Rates: Work Time Details

Math Lesson Book 3

 1 Percents Details 2 Profits Details 3 Permutation Combination Details 4 Probability Details 5 Geometry Details 6 Solid Geometry 7 Coordinate Geometry Details