Linear Equation Word Problems: Two Boats start 100 miles apart and start moving...

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spaceshowfeature1

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Hi! I’m now solving Linear Equation Word Problems. Here is one I’ve had trouble with: “Two Boats start out 100 miles apart and start moving to the right at the same time. The boat on the left is moving at twice the speed as the boat on the right. Five hours after starting the boat on the left catches up on the right. How fast was each boat moving?”

I don’t even know where to start. I try to think up a diagram, but it ends up being wrong, because I can’t imagine the situation. How can I imagine this situation, and get a diagram out? Then comes another difficult part, setting up the equation. How can I do that? I know part of the answer is lots of practice, but how can I practice when I don’t even know what to do? That leads into my next point: Where can I find practice problems similar to these? I’m using Paul’s online notes, and I’m runing out of practice problems.

Thanks and good day.
 
spaceshowfeature1 said:
Hi! I’m now solving Linear Equation Word Problems. Here is one I’ve had trouble with: “Two Boats start out 100 miles apart and start moving to the right at the same time. The boat on the left is moving at twice the speed as the boat on the right. Five hours after starting the boat on the left catches up on the right. How fast was each boat moving?”

I don’t even know where to start. I try to think up a diagram, but it ends up being wrong, because I can’t imagine the situation. How can I imagine this situation, and get a diagram out? Then comes another difficult part, setting up the equation. How can I do that? I know part of the answer is lots of practice, but how can I practice when I don’t even know what to do? That leads into my next point: Where can I find practice problems similar to these? I’m using Paul’s online notes, and I’m runing out of practice problems.

Thanks and good day.
Click to expand...
Almost all the word problems start with answers to the following questions.

What do you need to find? - speed of each boat

What is given to you? Two statements:

1) The boat on the left is moving at twice the speed as the boat on the right

2) Two Boats start out 100 miles apart and start moving to the right at the same time

So from our find - we have two unknowns.

The speed of the boat on the right = R =......................................................(1)

The speed of the boat on the left = L ......................................................(2)

What is the relationship between the speed (the unknown) and the given

distance = speed * time .........................................................................(3)

It is also given L = 2*R...........................................................................(4)

Suppose the two boats meet at time 't' after starting.

So

After time 't', the left boat would have travelled a distance of = t * L .............(5)

After time 't', the right boat would have travelled a distance of = t * R .............(6)

Now continue.......
 
Subhotosh Khan said:
Almost all the word problems start with answers to the following questions.

What do you need to find? - speed of each boat

What is given to you? Two statements:

1) The boat on the left is moving at twice the speed as the boat on the right

2) Two Boats start out 100 miles apart and start moving to the right at the same time

So from our find - we have two unknowns.

The speed of the boat on the right = R =......................................................(1)

The speed of the boat on the left = L ......................................................(2)

What is the relationship between the speed (the unknown) and the given

distance = speed * time .........................................................................(3)

It is also given L = 2*R...........................................................................(4)

Suppose the two boats meet at time 't' after starting.

So

After time 't', the left boat would have travelled a distance of = t * L .............(5)

After time 't', the right boat would have travelled a distance of = t * R .............(6)

Now continue.......
Click to expand...

Why do the boats travel t*L and t*R? I don’t know what to do. I’m sorry.
 
spaceshowfeature1 said:
Hi! I’m now solving Linear Equation Word Problems. Here is one I’ve had trouble with: “Two Boats start out 100 miles apart and start moving to the right at the same time. The boat on the left is moving at twice the speed as the boat on the right. Five hours after starting the boat on the left catches up on the right. How fast was each boat moving?”
Click to expand...
With these, making up a simple diagram is half the solution!
(v = right boat speed)
|...............100...............|@v----------5v------------->5

|@2v---------------------10v----------------------------->5

100 + 5v = 10v

Get my drift?
 
Last edited:
spaceshowfeature1 said:
Hi! I’m now solving Linear Equation Word Problems. Here is one I’ve had trouble with: “Two Boats start out 100 miles apart and start moving to the right at the same time. The boat on the left is moving at twice the speed as the boat on the right. Five hours after starting the boat on the left catches up on the right. How fast was each boat moving?”

I don’t even know where to start. I try to think up a diagram, but it ends up being wrong, because I can’t imagine the situation. How can I imagine this situation, and get a diagram out? Then comes another difficult part, setting up the equation. How can I do that? I know part of the answer is lots of practice, but how can I practice when I don’t even know what to do? That leads into my next point: Where can I find practice problems similar to these? I’m using Paul’s online notes, and I’m runing out of practice problems.

Thanks and good day.
Click to expand...

as suggested, your first step is draw a picture, to scale is best.
 
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