Question 990057
I have some tips for word problems:
(1) Every word MAY be important -read carefully
(2) Right away, state that x = the unknown they
are looking for. This really helps.
(3) You might start at the end of what they give you
and start the solution from there- you don't 
alway work in a straight line.
(4) Is it a mixture problem? Is it a rate problem?
Is it a work problem? Put it in a category
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What you have is a rate problem. It's not worded
very well because it should say that the plane is
flying at a constant speed, so I'll have to assume that.
Sometimes, I put down a formula in words instead of
symbols like for this problem:
[ change in distance ] / [ change in time ] = [ average speed ]
{{{ ( 1800 - 2000 ) / ( 14 - 10 ) }}}
{{{ -200 / 4 = -50 }}} meters / sec
The minus sign doesn't matter in this case, I just need the speed
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They want to know, after {{{ s }}} seconds, how far in meters is
the plane from her
If {{{ m }}} is distance in meters from her, I can say:
{{{ s }}} = flying time in seconds
{{{ m }}} = meters from her
{{{ 2000 - m = 50*( s - 10 ) }}} answer
Does this really work?
After flying for {{{ 10 }}} sec, 
{{{ 2000 - m = 50*( 10 - 10 ) }}}
{{{ 2000 - m = 50*0 }}}
{{{ 2000 - m = 0 }}}
{{{ m = 2000 }}} distance from her in meters
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After flying for {{{ 14 }}} sec,
{{{ 2000 - m = 50*( 14 - 10 ) }}}
{{{ 2000 - m = 50*4 }}}
{{{ 2000 - m = 200 }}}
{{{ m = 2000 - 200 }}}
{{{ m = 1800 }}}
It works
It helps if you can plot the equation, or try to
visualize what the plot would look like in order
to search for an equation.
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Here's the plot:
I'll just clean up the equation:
{{{ 2000 - m = 50*( s - 10 ) }}}
Add {{{ m }}} to both sides
{{{ 2000 = m + 50*( s - 10 ) }}}
Subtract {{{ 50*( s - 10 ) }}} from both sides
{{{ -50*( s - 10 ) + 2000 = m }}}
{{{ m = -50s + 500 + 2000 }}}
{{{ m = -50s + 2500 }}}
{{{ graph( 400, 400, -10, 70, -400, 4000, -50x + 2500 ) }}}
Hope this isn't too confusing-
keep plugging away -that's what
I've always had to do!