Question

It takes a boat 3 hours to travel with the current 90 miles. It takes the same boat traveling the same speed 5 hours to travel back against the current. What is the speed of the boat and how fast is the current?

Answer 1

The speed of the boat is 24 mph and the speed of the current is 6 mph.

Step-by-step explanation:

To find the speed of the boat and the speed of the current, we can use the concept of relative velocities. Let's assume that the speed of the boat in still water is 'b' and the speed of the current is 'c'.

When the boat is traveling with the current, its effective speed is increased by the speed of the current, so we have (b+c) = 90/3 = 30 mph.

When the boat is traveling against the current, its effective speed is decreased by the speed of the current, so we have (b-c) = 90/5 = 18 mph.

Solving these two equations, we can find the values of 'b' and 'c' as follows:

Adding the two equations: (b+c) + (b-c) = 30 + 18 => 2b = 48 => b = 24 mph

Subtracting the second equation from the first: (b+c) - (b-c) = 30 - 18 => 2c = 12 => c = 6 mph

Therefore, the speed of the boat is 24 mph and the speed of the current is 6 mph.