A tourist sailed against the current on a river for 6 km, and then he sailed in a lake for 15 km. In the lake he sailed for 1 hour longer than he sailed in the river. Knowing that the current of the river is 2 km/hour, find the speed of the boat while it is traveling in the lake.
rate of sailing in still water , assuming the lake has no current ---- x km/h
rate of sailing in river against current -- x-2 km/h
time in river = 6/(x-2)
time in lake = 15/x
the difference in those times is = 1
form the equation and solve for x
hint: I would multiply each term by x(x-2) to eliminate the fractions.
Let me know what you get.
To find the speed of the boat while it is traveling in the lake, we need to first calculate the time it took for the boat to sail in the river.
Let's assume the speed of the boat in still water is 'x' km/hour.
Since the boat sailed against the current in the river, we need to subtract the speed of the current from the speed of the boat to get the effective speed.
Effective speed in the river = Speed of the boat - Speed of the current
= x - 2 (since the current is 2 km/hour)
The time taken to sail in the river can be calculated as the distance divided by the effective speed.
Time taken in the river = Distance / Effective speed in the river
= 6 km / (x - 2) km/hour
Given that the boat sailed in the lake for 1 hour longer than in the river, the time taken in the lake can be expressed as:
Time taken in the lake = Time taken in the river + 1 hour
= 6 km / (x - 2) km/hour + 1 hour
Since we know the time taken in the lake, we can use it to find the speed of the boat in the lake.
The distance traveled in the lake is given as 15 km.
Speed = Distance / Time
Speed of the boat in the lake = 15 km / [6 km / (x - 2) km/hour + 1 hour]
Simplify further to get the final answer.