A boat moves downstream at the rate of 8 km/hr, and upstream at 4 km/hr. The speed of the boat in still waters is:
6 km/hr
Let's denote:
- \(v_b\): speed of the boat in still water (km/hr)
- \(v_s\): speed of the stream (km/hr)
When the boat moves downstream, the speed of the boat is the sum of its speed in still water and the speed of the stream:
\(v_{down} = v_b + v_s = 8\) km/hr
When the boat moves upstream, the speed of the boat is the difference between its speed in still water and the speed of the stream:
\(v_{up} = v_b - v_s = 4\) km/hr
We have a system of two linear equations with two unknowns:
\(v_b + v_s = 8\)
\(v_b - v_s = 4\)
Adding the two equations, we get:
\(2v_b = 12\)
Solving for \(v_b\):
\(v_b = \frac{12}{2} = 6\) km/hr
Therefore, the speed of the boat in still water is 6 km/hr.
Similar Questions
If (233)2 = 4x then 3x is equal to:
The value of \(\frac{(2.3)^3 + 0.027}{(2.3)^3 - 0.69 + 0.09}\) is
The value of (1 - √2) + (√2 - √3) + (√3 - √4) + ..... + (√15 - √16) is
The cube of 105 is
At an average of 80 km/hr Shatabdi Express reaches Ranchi from Kolkata in 7 hrs. Then the distance between Kolkata and Ranchi is
If \( x + \frac{1}{x} = 5 \), then the value of \( \frac{5x}{x^2 + 5x + 1} \) is
The cube of 997 is:
If ( x - 5)2 + (y - 2)2 + (z - 9)2= 0 , then value of (x + y - z) is
A motor cycle gives an average of 45 km per litre. If the cost of petrol is Rs. 20/litre. The amount required to complete a journey of 540 km is:
If \(\sqrt{3}\)=1.732 , then the value of \(\frac{9 + 2\sqrt{3}}{\sqrt{3}}\) is:
Important Questions from Simplification
If P = 0.3 × 0.3 + 0.03 × 0.03 - 0.6 × 0.03 and Q = 0.54, then \(\rm \frac{P}{Q}\) is equal to:
The value of \(\left(\frac{1}{2}\right)^{−2} \times\left(\frac{1}{3}\right)^{−2} \times\left(\frac{1}{4}\right)^{−2} \) is
The solution of the equation \(\frac{2}{3 x-4}+\frac{2}{2 x-6}=0 \) is:
If \(\rm \sqrt{1225 \times \sqrt{32 \div x}}= 70\) find the value of x.
What will come in the place of question mark (?) in the given expression?
\(\sqrt{21+\sqrt{49}+\sqrt{64}} \space {\%\:of\:5000}=?\)
