The boat sails along the river, the speed of which is 2 km / h. For 6 hours along the river and 8 hours

The boat sails along the river, the speed of which is 2 km / h. For 6 hours along the river and 8 hours against the current, the boat sailed 164 km. How long will it take for him to swim 54 km on the lake if he swims at the same speed?

1) Find the boat’s own speed.
Let the boat’s own speed be equal to x km / h, then the speed of the boat along the river is (x + 2) km / h, and the speed of the boat against the current is (x – 2) km / h. In 6 hours the boat will pass 6 (x + 2) km along the river, and in 8 hours it will pass 8 (x – 2) km against the river. According to the condition of the problem, it is known that the boat will pass (6 (x + 2) + 8 (x – 2)) km or 164 km in total. Let’s make an equation and solve it.
6 (x + 2) + 8 (x – 2) = 164;
6x + 12 + 8x – 16 = 164;
14x – 4 = 164;
14x = 164 + 4;
14x = 168;
x = 168: 14;
x = 12 (km / h).
2) Let’s find how long it will take for the boat to go 54 km on the lake. To find the time, the distance must be divided by the speed.
54: 12 = 4.5 (h).
Answer. 4.5 hours.