Aboat travels 33 miles downstream in 4 hours. the return trip takes the boat 7 hours. find the speed of the boat in still water.

Speed of the boat in still water = 6.125 miles/hour

Step-by-step explanation:

We are given that a boat travels 33 miles downstream in 4 hours and the return trip takes the boat 7 hours.

We are to find the speed of the boat in the still water.

Assuming to be the speed of the boat in still water and to be the speed of the water.

The speeds of the boat add up when the boat and water travel in the same direction.

And the speed of the water is subtracted from the speed of the boat when the boat is moving upstream.

Adding the two equations to get:

+  

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Solving this equation for and substituting the given values for :

Therefore, the speed of the boat in still water is 6.125 miles/hour.

Step-by-step explanation:

Let' call "b" the speed of the boat and "c" the speed of the river.

We know that:

Where "V" is the speed, "d" is the distance and "t" is the time.

Then:

We know that distance traveled downstream is 33 miles and the time is 4 hours. Then, we set up the folllowing equation:

For the return trip:

   (Remember that in the return trip the speed of the river is opposite to the boat)

By solving thr system of equations, we get:

- Make both equations equal to each other and solve for "c".

- Substitute "c" into any original equation and solve for "b":