Solve Line Intersection Word Problem: Car A vs Car B

[scotty2024]

How can I create two functions out of the following word problem to figure out where they intersect?

Word problem:
If car A gets 33mpg but costs $3.43 per gallon and car B gets 42mpg and costs $4.06 per gallon, at what distance is it better to drive car A than car B and at what distance is it better to drive car B than car A?

Thanks.

 

[tiny-tim]

hi scotty2024!

i don't get it …

those figures give you a fixed miles-per-dollar for each car …

have you left something out of the question? ​

 

[scotty2024]

I'll try to explain it better.

Car A get worse gas millage than car B. Car A get 33 miles per gallon and car B gets 42 miles per gallon. Car A costs $3.43 per gallon of fuel used to operate, car B costs $4.06 per gallon used to operate. So if car A drives 33 miles it will cost the user $3.43. If car B drives 42 miles it will cost $4.06 to operate. So the question is, at what millage does it cost the same to operate car A as it does car B, and at what distance (millage) is car A more cost efficient compared to car B, and at what distance (millage) is car B more cost efficient compared to car A?

Does that make more sense?

 

[tiny-tim]

it makes the same sense as before …

it still gives a fixed miles-per-dollar for each car ​

 

[scotty2024]

I think I see what you are saying. My thinking was that if it always costs car A 3.34 per gallon and car B 4.06 per gallon and the two cars had different millage, car A would be more efficient at short distances than car B. But if each car drove 1 mile it would still be more efficient to drive car B. For example it costs car B 0.097 cents (4.06/42) to drive one mile and car A 0.104 cents (3.43/33) to drive one mile. 0.097x < 0.104x so this would mean that at any distance car B is more efficient. Is this correct?

I was thinking that I could plot two lines (such as y1 = 0.104x + 3.43 and y2 = 0.097x + 4.06) to figure out the best car to drive for a given distance.

 

[tiny-tim]

… For example it costs car B 0.097 cents (4.06/42) to drive one mile and car A 0.104 cents (3.43/33) to drive one mile. 0.097x < 0.104x so this would mean that at any distance car B is more efficient. Is this correct?

yes!

I was thinking that I could plot two lines (such as y1 = 0.104x + 3.43 and y2 = 0.097x + 4.06) to figure out the best car to drive for a given distance.

if those were the right equations, that would certainly work, but on the facts given, they're not

 

[scotty2024]

So what are the two equations? Are they y1 = 0.097x and y2 = 0.104x?

 

[tiny-tim]

yup!

 

[scotty2024]

Thanks a lot!

 

[SteamKing]

It's like the old joke, "We lose x dollars on every unit we sell, but we make up the difference on volume!"