Traveling downstream a certain boat went 21 mph. Traveling upstream it went only 5 mph. Find the speed of the boat in still water and the speed of the current.

speed of boat --- x

speed of current -- y

x+y = 21
x-y = 5

add the two equations, and continue

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Traveling downstream a certain boat went 21 mph. Traveling upstream it only went 1 mph. Findthe current and the speed of the boat if there were no current.

Traveling downstream a certain boat went 21 mph. Traveling upstream it only went 11 mph.

To find the speed of the boat in still water and the speed of the current, we need to set up a system of equations based on the information given.

Let's denote the speed of the boat in still water as 'b' and the speed of the current as 'c'.

When traveling downstream, the speed of the boat will be increased by the speed of the current. So, the effective speed while going downstream would be 'b + c'.

Similarly, when traveling upstream, the speed of the boat will be decreased by the speed of the current. Thus, the effective speed while going upstream would be 'b - c'.

From the information given in the question, we can set up the following equations:

1) b + c = 21 (speed downstream)
2) b - c = 5 (speed upstream)

We can solve this system of equations to find the values of 'b' and 'c'. To do so, we can add the two equations together:

(b + c) + (b - c) = 21 + 5

This simplifies to:

2b = 26

Dividing both sides by 2, we find:

b = 13

Now, we can substitute the value of 'b' back into one of the original equations, such as equation 1, to solve for 'c':

13 + c = 21

Subtracting 13 from both sides, we get:

c = 8

Therefore, the speed of the boat in still water is 13 mph, and the speed of the current is 8 mph.