# The first boat has a speed 10 km / h less than the second boat.

The first boat has a speed 10 km / h less than the second boat. What is the speed of the first boat if it crosses a lake 60 km wide in 12 minutes more than the second?

Let’s take the speed of the second boat V km / h, then the speed of the first (V-10) km / h.
Time to swim across the lake 60 / V and 60 / (V-10), respectively.
Knowing that 12 minutes is 1/5 of an hour, we can make the equation:
60 / (V-10) -60 / V = 1/5;
(300V-300V + 3000) / (V * (V-10) * 5) = (V²-10V) / (V * (V-10) * 5);
V²-10V-3000 = 0;
Solving the quadratic equation by Vieta’s theorem,
V = 60 or V = -50 (does not satisfy the problem condition)
Knowing that the speed of the second boat is 60 km / h, we calculate the speed of the first boat:
60-10 = 50 (km / h)

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