The arithmetic mean of the speeds upstream and upstream of the boat is 8.5 km / h.

| September 20, 2021 | education

The arithmetic mean of the speeds upstream and upstream of the boat is 8.5 km / h. boat speed along the river 10.9 km / h. What is the speed of the river current? What is the speed of the boat against the current?

Let the speed of the river flow x (x) km / h, then the boat’s own speed is (10.9 – x) km / h, and against the current – (10.9 – x – x) km / h. Knowing that the arithmetic mean of the boat speeds upstream and upstream is 8.5 km / h, we will compose the equation:
(10.9 + 10.9 – x * 2): 2 = 8.5;
21.8 – x * 2 = 8.5 * 2;
21.8 – x * 2 = 17;
– x • 2 = 17 – 21.8;
– x • 2 = – 4.8;
x • 2 = 4.8;
x = 4.8: 2;
x = 2.4 (km / h) – the speed of the river.
Let’s calculate the speed of the boat against the current: 10.9 – x • 2 = 10.9 – 2.4 • 2 = 6.1 (km / h).
Answer: the speed of the river flow is 2.4 km / h, and the speed of the boat against the current is 6.1 km / h.



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