Class X: Mathematics - A Boat Goes Upstream and Downstream Word Problem

Class: 10
Subject: Mathematics
Chapter: Pair of Linear Equations in Two Variables
Topic: Solving word problems using a pair of linear equations in two variables
Curriculum & Board: NCERT & CBSE 
Focus Group: Visual and Auditory Learners 
Methodology: Audio Video Presentation on White Board 
Teaching Strategy: Step by Step (Using Task Analysis)

A step-by-step guide ('no shortcuts') to solving a word problem involving a boat going upstream and downstream using a pair of linear equations: 
Step 0. Problem Statement 
Introduces the word problem where a boat travels upstream and downstream, and the goal is to determine the speed of the stream and the boat in still water.
Step 1: Identify Unknowns
Explains how to identify the unknown quantities (speed of the stream and speed of the boat in still water) and represent them with variables (x and y). It also clarifies the units (kilometers per hour).
Step 2: Understand Dynamics of Boat Movement 
Discusses how the speed of the boat is affected by the stream's current. The effective speed downstream is x + y (boat speed + stream speed), and upstream is x - y (boat speed - stream speed).
Step 3: Formulate Linear Equations
Shows how to use the given information (distance and total time for both scenarios) and the formula time = distance / speed to create two linear equations.
Step 4: Substitution for Simplification
Introduces a substitution method (letting 1/(x-y) = u and 1/(x+y) = v) to transform the complex equations into a more standard form of linear equations.
Step 5: Solve for Substituted Variables (u and v) 
Demonstrates how to solve the new pair of linear equations for 'u' and 'v' using the elimination method.
Step 6: Solve for Original Variables (x and y)
Uses the calculated values of 'u' and 'v' to find the actual speeds of the boat in still water (x) and the stream (y) by setting up two new simpler equations.
Step 7: Final Answer
Presents the final answer for the speed of the boat in still water (8 km/h) and the speed of the stream (3 km/h).
Recap: Briefly reviews the entire problem-solving process.

Note 
+ This video is meant to serve as a guide for children studying in Class X on how to approach word problems in Mathematics in a systematic and logical manner.   

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Acknowledgements 
+ Grace of God
+ Family 
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+ Teachers, Students, Mentors | Professors and Fellow Educators | Colleagues 

May the Force be with you. 

With Hope.