 # Math Book 2: Rates: Speed Distance

GMAT® Study Material for Speed - Time - Distance

S peed time distance, one of the three parts of rates, brings one to two questions to the table. GMAT tests both problems and data sufficiency questions from this topic.

### Concepts Covered

It is an important topic and includes relationship between speed, time, distance. Watch out for different units of measurement used for speed, time and distance and convert them to bring uniformity of units before starting your computation. Also included are concepts on average speed and relative speed. Wizako's GMAT Math Lesson Book in this chapter covers the following concepts:

1. Common units of measurement for distance, time and speed.
2. The relationship between speed, distance and time has been highlighted and for better understanding of the concept illustrative examples have been provided.
3. Simple conversion factors for different units of speed, time and distance such as conversion between mph to kmph or m/sec.
4. Method to calculate average speed under three different scenarios has been explained along with examples.
5. Definition of the term relative speed and the method of calculation when traveling in the same direction and different directions are explained.
6. How to compute speed when a boat travels in a stream that is flowing or an aircraft that has a tailwind?
7. 23 solved examples in speed distance and time are included with detailed explanation. Shortcuts that can be used to arrive at the result quicker have been mentioned wherever applicable.
8. In addition, boats in streams (Upstream and downstream) have been explained and to aid the understanding process 5 solved examples have also been worked out
9. 24 exercise problems with answers and explanation have been provided to gain practice.
10. A multiple choice test with 44 GMAT level questions has been included in the work book. All questions have been provided with detailed explanatory answers.

Here is a typical solved example from this chapter.

### Sample Question

A boat travels upstream at a speed of 30 mph and then downstream at a speed of 45 mph. What is the speed of the boat in still water and what is the speed of the stream?

Downstream journey: The boat and the stream are traveling in the same direction. So, the stream aids the movement of the boat.
Upstream journey: The boat and the stream are traveling in opposite directions. So, the stream cuts down the speed of the boat.

Downstream speed of the boat (D) = Speed of boat in still water (B) + speed of stream (S)
Upstream speed of the boat (U) = Speed of boat in still water (B) - speed of stream (S)

Upstream speed = 30 mph
B - S = 30 ... (1)

Downstream speed = 45 mph
B + S = 45 ... (2)

Solve for B by adding equations (1) and (2)
B - S = 30
B + S = 45
---------------
2B = 75
---------------
Or B, speed of the boat in still water = 37.5 mph

Substitute B = 37.5 in equation (1)
37.5 - S = 30
Or S, speed of the stream = 7.5 mph

### 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