- Rational and Irrational Numbers
- Compound Interest
- Expansions
- Factorization
- Simultaneous Linear Equations
- Problems on Simultaneous Linear Equations
- Quadratic Equations
- Indices
- Logarithms
- Triangles
- Mid Point Theorem
- Pythagoras Theorem
- Rectilinear Figures
- Theorems on Area
- Circle
- Mensuration
- Trigonometric Ratios
- Trigonometric Ratios and Standard Angles
- Coordinate Geometry
- Statistics
ML Aggarwal Solutions Class 9 Mathematics Solutions for Problems on Simultaneous Linear Equations Exercise 6 in Chapter 6 - Problems on Simultaneous Linear Equations
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A boat takes 2 hours to go 40 km down the stream and it returns in 4 hours. Find the speed of
the boat in still water and the speed of the stream.
Let’s assume the speed of the boat in still water be x km/hr
And the speed of the stream = y km/hr
So, the speed of the boat in downstream = (x + y) km/hr
The speed of the boat in upstream = (x - y) km/hr
We know,
Distance = Speed x time
Now, according to the given conditions in the problem, we have
40 = (x + y) × 2
x + y = 20 … (i)
And,
40 = (x - y) × 4
x – y = 10 … (ii)
Adding (i) and (ii), we have
x + y = 20
x – y = 10
2x = 30
x = 15
On substituting the value of x in equation (i), we have
15 + y = 20
y = 20 – 15
y = 5
Therefore, speed of the boat in still water = 15 km/hr and speed of the stream = 5 km/hr.
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