Answer:
The speed of the boat is 7 km/h and thes peed of the current is 5 km/h;
Step-by-step explanation:
We don't know neither the speed of the boat nor the speed of the current, so let:
speed of the boat = x;
speed of the current = y;
If the boat is travelling with the current we know that those two speed are adding up, therefore we can conclude that:
x + y = 12;
But If the boat is travelling against the current we know that we have to subtract them, therefore:
x - y = 2;
Now we've a system of equations with the same two variables, therefore, by substitution method (or any other method) we can find the variables:
[tex]\left \{ {{x +y = 12} \atop {x - y = 2}} \right.[/tex]
So using the first equation, we get that:
[tex]x = 12 - y[/tex]
And substituting that x to the second equation we get:
[tex]x - y = 2\\(12 - y) - y = 2\\12 - 2y = 2\\12 - 2 = 2y\\10 = 2y\\5 = y[/tex]
So we can conclude that the speed of the current is 5 km/h.
And now with that answer, using equation 1, we can solve the speed of the boat.
[tex]x + y = 12\\x + 5 = 12\\x = 12 -5\\x = 7[/tex]
