The ratio of the own speed of the motor ship to the speed of the river flow is 10: 1.

The ratio of the own speed of the motor ship to the speed of the river flow is 10: 1. The own speed of the motor ship is 24.3 km / h more than the speed of the current. How far will the motor ship sail in 3 hours along the river?

Brief notation of the problem condition:
ϑ motor ship ∶ ϑ current = 10: 1;
ϑ motor ship> ϑ current at 24.3 km / h;
t – 3 hours;
S -?
Decision:
1) Let x km / h be the own speed of the motor ship, and y km / h the speed of the river. Since, according to the condition of the problem, the own speed of the motor ship refers to the speed of the river flow as 10: 1, then we will compose the first equation:
x: y = 10: 1;
Since the speed of the ship is 24.3 km / h more than the speed of the current, then we will compose the second equation:
x – y = 24.3;
We have a system of equations:
x: y = 10: 1;
x – y = 24.3;
Let us find the value of x from the first equation.
x = 10y;
We substitute the found value of x into the second equation.
x – y = 24.3;
10y – y = 24.3;
9y = 24.3;
y = 24.3: 9;
y = 2.7 (km / h);
If y = 2.7, then x = 10y = 10 * 2.7 = 27 (km / h);
2) The speed of the ship along the river is equal to the sum of the ship’s own speed and the speed of the river.
ϑ downstream = ϑ motor ship + ϑ current;
ϑ downstream = 27 + 2.7 = 29.7 (km / h);
3) To find the distance that the ship will sail along the river, you need to multiply the speed of the ship along the river by the time of its movement.
S = ϑ downstream * t;
S = 29.7 * 3 = 89.1 (km)
Answer: 89.1 km.