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 - Straight Races and Circular Races. 4GMAT'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 are given to explain the above mentioned concept
4. 9 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. An objective type speed test with around 40 questions with explanatory answers and answer key provided for the speed test
Here is an example of a typical solved example in this chapter.
Sample Question
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 15m/min and 'Q' runs at a speed of 10m/min, when will they meet again for the first time?
Explanatory Answer
As P and Q run in the same direction, their relative speed = 15 - 10 = 5 m/min
Circumference of the circular track is the length of the circular track = 2 * pi * r = 2 * (22/7) * 49 = 308 m.
Time taken for the two of them to meet for the first time after they have started a race along a circular track, starting simultaneously from the same point is given by
(length of the circular track / relative speed) = 308 / 5 = 61.6 minutes
Therefore, they will meet for the first time after 1 hour, 1 minute and 36 seconds.
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