Question

A river cruise boat sailed 96 miles down the Mississippi River for four hours. It took six hours to return. Find the rate of the cruise boat in still water and the rate of the current.

Answer 1

Explanation:

Let's use the formula:

distance = rate x time

Let's denote the rate of the cruise boat in still water as "r" and the rate of the current as "c".

When the boat is going downstream, it has the speed of the still water plus the speed of the current. When it is going upstream, its speed is the still water speed minus the current speed.

So, we have two equations based on the distance travelled:

Downstream: 96 = (r + c) x 4

Upstream: 96 = (r - c) x 6

We can solve this system of equations by simplifying the first equation to r + c = 24, and the second equation to r - c = 16.

We can add these two equations to eliminate c and get 2r = 40, so r = 20.

We can then substitute r = 20 into one of the original equations to find c. Let's use r + c = 24, which gives c = 4.

So, the rate of the cruise boat in still water is 20 miles per hour, and the rate of the current is 4 miles per hour.