SOLUTION: Boating: The table gives the amount of y gas needed to travel a fixed distance if a boat gets x miles per gallon when driven at a constant speed.
Mileage (miles per gallon), x
Algebra.Com
Question 828298: Boating: The table gives the amount of y gas needed to travel a fixed distance if a boat gets x miles per gallon when driven at a constant speed.
Mileage (miles per gallon), x = 11 Gas (gallons) y =7.5
Mileage (miles per gallon), x = 13.75 Gas (gallons) y =6
Mileage (miles per gallon), x = 15 Gas (gallons) y =5.5
Mileage (miles per gallon), x = 16.5 Gas (gallons) y =5
Mileage (miles per gallon), x = 27.5 Gas (gallons) y =3
Mileage (miles per gallon), x = 33 Gas (gallons) y =?
I am not sure how to figure this out. For the last part x=33 y=? I guessed that y would be 2.5. I am not sure how I arrived at that answer. I looked a a pattern with the Ys. If it was x was a whole number, the y would be a decimal. If Y as a decimal then y was a whole number. The Ys were in descending order.
Please explain how to do that answer.
Thank you!
Found 2 solutions by TimothyLamb, KMST:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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the given data is not linear, which you can verify as follows:
11 7.5
13.75 6
15 5.5
16.5 5
27.5 3
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copy and paste the above data into this linear regression solver:
https://sooeet.com/math/linear-regression.php
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as you can see, the given data points do not fit the line perfectly, but you can use the line as a linear model of the given data, and use the linear model to estimate y for x=33 as follows:
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linear model:
b = y-intercept = 9.54191291
m = slope = -0.247278383
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slope-intercept form of linear model:
y = -0.247278383x + 9.54191291
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y(33) = -0.247278383*33 + 9.54191291
y(33) = 1.381726271000002
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answer:
if the boat gets 33 mpg, to travel the fixed distance the boat would be needed about 1.4 gallons of fuel
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
AS A MATH CLASS PROBLEM:
If this is a problem for a math class in school, you are probably expected to do it a certain way, following a certain procedure, and/or using a certain formula, rather than using your brain. That kind of "educational malpractice" causes many brains to atrophy, and convinces many people that doing well in math (and physics) is just a question of memorizing a lot of facts and formulas. So wrong, so sad!
You are probably expected to think of this as an "inverse' relation, as in
"for a certain fixed distance, the number of gallons of fuel consumed is inversely proportional to the mileage (miles per gallon) of the vehicle"
The more economic your vehicle (yielding more miles per gallon of fuel), the less fuel you will need to go from home to work, or from home to school.
If you use a small car that gives you twice as many miles per gallon as your neighbors big pick up truck, you will use half the amount of fuel your neighbor uses.
You probably were given the formula for when is inversely proportional to .
You were probably told that is a constant,
and that if you know one (x,y) pair in that relationship, you can find all the others.
Take, for example,
Mileage (miles per gallon), x = 15 Gas (gallons) y =5.5
Substituting those values into
we find as an equation to solve for .
--> -->
Now you have a relation (and more specifically, a function) to calculate for any :
So, for ,
-->
Indeed, you can build the whole table with that "formula", which makes me wonder why they gave you so many lines in that table.
AS AN SAT PROBLEM:
In this case, you are expected to use your brain, and forget formulas.
Think as a fifth grader should be able to think.
If the guy with the inefficient boat doing just x=16.5 miles per gallon needs y=5 gallons to go a certain distance,
your twice as efficient boat, doing twice as many miles per gallons (x=33), will need half as much fuel:
.
IF YOU HAD JUST A TABLE of x and y values (maybe data collected from a science lab experiment), you would want to plot your data, and would get
Excel, or any statistical software package would let you make that graph and calculate best fit curves for several models (theories on whether y varies linearly with x, or with x squared, or it is an exponential function, or some other relation). It will tell you that the linear model does not fit very well,
but you can see that the points do not fit a straight line. They suggest a curve. If the statistic program had an inversely proportional model, it would tell you that it fits the data perfectly.
Otherwise, if you were in calculus, or pre-calculus class you might say the plotted points make the relation look like a hyperbola, with the x- and y-axes as aymptotes.
So you would try to plot against . Then you would find an absolutely perfect linear fit, and would realize that real data cannot be that perfect. Your lab partner must have fabricated the data.
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