Isolate  in the first equation.

Plug into the second equation to solve for .

Plug into the first equation to solve for .

Now we have both the and values and can express them as a point: .

1st equation:

2nd equation:

Subtract the 2nd equation from the 1st equation to eliminate the "2y" from both equations and get an answer for x:

Plug the value of  into either equation and solve for :

Substitute equation 2. into equation 1.,

so, 

Substitute  into equation 2:

so, the solution is .

This problem is a system of equations, and uses the equation .  

Start by assigning variables. Let  stand for the rate of the boat, let  stand for the rate of the current.  

When the boat is going upstream, the total rate is equal to .  You must subtract because the rates are working against each other—the boat is going slower than it would because it has to work against the current.

Using our upstream distance (400m) and time (2hr) from the question, we can set up our rate equation:

When the boat is going downstream, the total rate is equal to  because the boat and current are working with each other, causing the boat to travel faster.

We can refer to the downstream distance (600m) and time (2hr) to set up the second equation:

From here, use elimination to solve for  and .

1. Set up the system of equations, and solve for .

2. Subsitute  into one of the equations to solve for .

Step 1: Set up the equations

Let = Nick's age now
Let = Sarah's age now

The first part of the question says "Nick's sister is three times as old as him".  This means:

The second part of the equation says "in two years, she will be twice as old as he is then).  This means:

Add 2 to each of the variables because each of them will be two years older than they are now.

Step 2: Solve the system of equations using substitution

Substitute for in the second equation.  Solve for 

Plug into the first equation to find

Solve using elimination:

multiply the 2nd equation by two to make elimination possible
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subtract 2nd equation from the first to solve for
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Substitute  into either equation to solve for

There are two ways to solve this:

-The 1st equation can be mutliplied by  while the 2nd equation can be multiplied by  and added to the 1st equation to make it a single variable equation where

.

This can be plugged into either equation to get 

or

-The 2nd equation can be simplified to,

.

This value for  can then be substituted into the first equation to make the equation single variable in .

Solving, gives , which can be plugged into either original equation to get 

rearranges to

and

, so

In the second equation, you can substitute  for  from the first.

Now, substitute 2 for  in the first equation:

The solution is 

Use elimination, multiply the top equation by -4 so that you can eliminate the X's.

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Combine these two equations, and then you have;

Plug in y into one of the original equations and solve for x.

Your solution is .