algebra II math problem..?? desperate!?

Question

A car's fuel efficiency rating for city driving is a different constant from its fuel efficiency rating for highway driving. A certain car traveled 120 miles in the city and 280 miles on the highway using one tankful of 16 gallons of fuel. On the next tankful of fuel, the car traveled 220 miles in the city and 140 miles on the highway. What is the fuel efficieny rating for this car on the highway??

WITH WORK PLEASE!!! :)

Answer 1

They're trying to teach you to set up and solve simultaneous equations.

Equation One.
120/a + 280/b = 16
Equation Two.
220/a + 140/b = 16

Multiply Equation Two by 2 on both sides.
440/a + 280/b = 32
Subtract Equation One from this to get
440/a - 120/a + 280/b - 280/b = 32-16
320/a = 16
a = 20 (miles per gallon in the city)

Plug a=20 into Equation One.
120/20 + 280/b = 16
6 + 280/b = 16
280/b = 10
b = 28 (miles per gallon on the highway)

Alternatively, you can plug a=20 into Equation Two.
220/20 + 140/b = 16
11 + 140/b = 16
140/b = 5
b = 28 (miles per gallon on the highway)

The first job in this kind of problem is to recognize the situation you're working with and get the units sorted out so that they make sense dimensionally.

The second job in this kind of problem is structuring the equation so that every term and every factor is in its proper relationship to the others in the equation.

The third job is to eliminate all but one of the unknowns through algebraic operations. In order to do this, you must have at least as many equations as unknowns. In this problem, you do: you have two equations and two unknowns.

The fourth job is to solve for the last remaining unknown, making it known.

The remaining jobs involve using the now-known variable(s) to solve progressively for the other unknowns.

Answer 2

we'll keep it simple...
One tankful is a constant amount, 16 gallons... thus in baby words...
City Miles = CM, Highway Miles = HM
120 CM + 280 HM = 200CM +140 HM
thus
140 HM = 80 CM
or rather... the same amount of fuel used in 80 miles in the city will get you 140 miles on the highway...

Thus as mentioned...
16 gallons of fuel gives you 120 miles in the city and 280 miles on the highway...
120 CM = 80CM *1.5; replace CM with HM = (140HM)*1.5
= 210 HM
in total 16 gallons will get you 210 + 280 = 490 HM

THUS 1 gallon will get you 490/16 = you do the calculating

thus the answer is that many miles/gallon

and get a tutor if you're struggling in Math or something :)

Answer 3

Step a million: Distribute 4(2x-3) + 8(x-4) = 2(2x+6) is going to 8x-12 + 8x-32 = 4x +12 Step 2: Simplify by ability of combining comparable words: 8x-12 + 8x-32 = 4x-12 is going to 16x -40 4 = 4x -12 Step 3: circulate the x's to a minimum of one facet 16x-40 4 = 4x - 12 is going to: 12x-40 4 = -12 Step 4: clean up for x 12x-40 4=-12 (upload 40 4 to the two factors) 12x=32 Divide by ability of 12 x=2.6

Answer 4

Let fuel effeceincy rating in city be x and in highway be y.
The equations are 120x+280y=16;
220x+140y=16.
Solve and get the answers.

Answer 5

I assume this is talking about the same car, this question is impossible to answer.
There is no way a car can travel on a ratio of about 1:1.25 then on the next one go on a ratio of 1.15:1
Unless its one of those stupid problems where it never mirrors real life. I think you have to use X and Y or something to solve this problem.