Last updated at May 29, 2018 by Teachoo

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Example 19 A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water. Let the speed of boat in still water be x km/hr & let the speed of current(stream) be y km/hr Speed downstream = Speed of boat in still water + Speed of stream Speed downstream = x + y Speed upstream = Speed of boat in still water Speed of stream Speed upstream = x y Given that A boat goes 30 km upstream and 44 km downstream in 10 hours Time taken to go 30 km upstream + Time taken to go 44 km downstream ( 30 )/( ) + ( 44 )/( ) = 10 30/( ) + 44/( + ) = 10 Similarly, A boat goes 40 km upstream and 55 km downstream in 13 hours Time taken to go 40 km upstream + Time taken to go 55 km downstream ( 40 )/( ) + ( 55 )/( ) = 13 40/( ) + 55/( + ) = 13 Our equations are 30 (1/( ))+44(1/( + ))=10 (1) 40 (1/( ))+55(1/( + ))=13 (2) Solving 30u + 44v = 10 (3) 40u + 55v = 13 (4) From (3) 30u + 44v = 10 30u = 10 44v u = (10 44 )/30 Putting value of u in (4) 40u + 55v = 13 40((10 44 )/30)+55 =13 4((10 44 )/3)+55 =13 Multiplying both sides by 3 3 4((10 44 )/3)+"3 " 55 ="3 " 13 4(10 44v) + 165 = 39 40 176v + 165v = 39 176v + 165v = 39 40 11v = -1 v = ( 1)/( 11) v = 1/11 Putting v = 1/11 in equation (3) 30u + 44v = 10 30u + 44(1/11) = 10 30u + 4 = 10 30u = 10 4 30u = 6 u = 6/30 u = 1/5 So, u = 1/5 & v = 1/11 So, u = 1/5 & v = 1/11 But we need to find x & y We know that So, our equations become x y = 5 (6) x + y = 11 (7) From (6) x y = 5 x = 5 + y Putting value of x in (7) x + y = 11 (5 + y) + y = 11 5 + 2y = 11 2y = 11 5 2y = 6 y =6/2 y = 3 Put y = 3 in (6) x y = 5 x 3 = 5 x = 5 + 3 x = 8 So, x = 8, y = 3 is the solution of the given equation Hence Speed of boat in still water = x = 8 km/hr Speed of stream = y = 3 km/hr

Chapter 3 Class 10 Pair of Linear Equations in Two Variables

Example 6
Important

Example 10 Important

Example 11 Important

Example 13 Important

Example 14 Important

Example 19 Important You are here

Ex 3.2, 1 Important

Ex 3.2, 3 Important

Ex 3.2, 6 Important

Ex 3.2, 7 Important

Ex 3.5, 2 Important

Ex 3.6, 1 (i) and (ii) Important

Ex 3.6, 1 (iii) and (iv) Important

Ex 3.6, 1 (v) and (vi) Important

Ex 3.6, 1 (vii) and (viii) Important

Ex 3.6, 2 Important

Class 10

Important Questions for Exam - Class 10

- Chapter 1 Class 10 Real Numbers
- Chapter 2 Class 10 Polynomials
- Chapter 3 Class 10 Pair of Linear Equations in Two Variables
- Chapter 4 Class 10 Quadratic Equations
- Chapter 5 Class 10 Arithmetic Progressions
- Chapter 6 Class 10 Triangles
- Chapter 7 Class 10 Coordinate Geometry
- Chapter 8 Class 10 Introduction to Trignometry
- Chapter 9 Class 10 Some Applications of Trignometry
- Chapter 10 Class 10 Circles
- Chapter 11 Class 10 Constructions
- Chapter 12 Class 10 Areas related to Circles
- Chapter 13 Class 10 Surface Areas and Volumes
- Chapter 14 Class 10 Statistics
- Chapter 15 Class 10 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.