SOLUTION: suppose you can type four pages in 50 minutes and nine ages in an hour and forty minutes find a linear function for the number of pages produced, p , as a function of time, t. if

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: suppose you can type four pages in 50 minutes and nine ages in an hour and forty minutes find a linear function for the number of pages produced, p , as a function of time, t. if      Log On


   

Question 910166: suppose you can type four pages in 50 minutes and nine ages in an hour and forty minutes
find a linear function for the number of pages produced, p , as a function of time, t. if time is measured in minutes, what value of t make sense in this example
how many pages can be typed in two hours
interpret the slope of the function in practical terms
solve the function in (a) for time as a function of pages
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Plot number of pages typed on the vertical axis
Plot time in minutes on the horizontal axis
Let +p+ = number of pages typed
Let +t+ = time in minutes
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You are given 2 points on the straight line:
( 50, 4 )
( 100, 9 )
Note that 1 hr 40 min = 100 min )
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Use the general point-slope formula:
+%28+p+-+4+%29+%2F+%28+t+-+50+%29+=+%28+9+-+4+%29+%2F+%28+100+-+50+%29+
+%28+p+-+4+%29+%2F+%28+t+-+50+%29+=+5+%2F+50+
+%28+p+-+4+%29+%2F+%28+t+-+50+%29+=+1%2F10+
+10%2A%28+p+-+4+%29+=+t+-+50+
+10p+-+40+=+t+-+50+
+10p+=+t+-+10+
+p+=+%281%2F10%29%2At+-+1+
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(a) The slope means, that for every 1 extra page
typed, you need 10 more minutes
-----------------------------------
(b)
time as a function of pages:
+t%28p%29+=+10%2A%28+p+%2B+1+%29+
----------------------
check:
(100,9)
+t%28p%29+=+10%2A%28+p+%2B+1+%29+
+100+=+10%2A%28+9+%2B+1+%29+
+100+=+10%2A10+
+100+=+100+
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
suppose you can type four pages in 50 minutes and nine pages in an hour and forty minutes
find a linear function for the number of pages produced, p , as a function of time, t. if time is measured in minutes,
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You have 2 points (50,4) and (100,9)
slope = (9-4)/(100-50) = 1/10
Form: p = mt+b
Solve for "b"::
4 = (1/10)50 + b
b = -1Equation::
p = (1/10)t - 1
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what value of t make sense in this example?
Solve (1/10)t - 1 >= 0
t >= 10 minutes
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how many pages can be typed in two hours?
Solve:: p = (1/10)120 -1 = 11 pages
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interpret the slope of the function in practical terms
m = 1/10 means 1 page per 10 minutes or (1/10) page per minute
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solve the function in (a) for time as a function of pages
p = (1/10)t -1
(1/10)t = p+1
t = 10(p+1)
----
Cheers,
Stan H.