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Question 895777: A hybrid car uses 50 miles per gallon of gas while driving in the city and 40 miles per gallon on the highway. The car has a 15 gallon gallon tank.
a. write an equation using C for city and H for highway to represent the cars gallons of gas used in the city and the highway: im completely confused.
b. write an expression to represent the miles the hybrid car can achieve: i think it is 40H + 50(15-H) i dont think so though
c.using parts 1 & 2, write a combined simplified expression to represent the above situation: completely lost again
d. what is the minimum and maximum distances the car can go?
minimum: idk maximum: i think its 600 miles
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! H is the number of gallons the car will use when traveling on the highway.
C is the number of gallons the car will use when traveling in the city.
on one tank of gas, the car can use 15 gallons of gas.
this means that H + C = 15
from this equation, you can solve for H in terms of C to get H = 15 - C or you can also solve for C in terms of H to get C = 15 - H.
either one of these equation will be helpful later.
let's answer your questions part by part.
a. write an equation using C for city and H for highway to represent the cars gallons of gas used in the city and the highway:
number of miles the car can drive in the city = 50*C
number of miles the car can drive on the highway = 40*H
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b. write an expression to represent the miles the hybrid car can achieve on a tankful of gas:
number of miles the car can achieve is equal to:
50*C + 40*H, where H + C is equal to 15.
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c.using parts 1 & 2, write a combined simplified expression to represent the above situation:
i'm really not sure what they're driving at here either.
i believe you already accomplished this with part b.
you can solve for H in terms of C and you will get:
H = 15 - C.
replace h in the equation with 15 - C and you will get:
50*C + 40*(15-C)
the implicit assumption here is that H + C = 15 which was already stated above.
your equation of 50*(15-H) + 40*H would yield the same result.
you just solved for C in terms of H where I solved for H in terms of C.
50*C + 40*(15 - C) is equivalent to 50*(15 - H) + 40*H.
both would yield the same result.
if C = 10, then 50*C + 40*(15 - C) = 50*10 + 40*5
if H = 5, then 50*(15 - H) + 40*H = 50*10 + 40*5
same result.
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d. what is the minimum and maximum distances the car can go?
since the car achieves the greater number of miles when you are traveling in the city, then the maximum number of mile you can achieve is when C = 15 and H = 0 and the formula becomes:
50*15 + 40*0 = 750 miles.
since the car achieves the least number of miles when you are traveling on the highway, then the minimum number of miles you can achieve is when C = 0 and H = 15 and the formula becomes:
50*0 + 40*15 = 600 miles.
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