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if I drive a car 60 miles per hour on a full tank, it'll run for 5 hours. for every mile per hour I speed up, the car will run 10 min less. for every mile per hour I slow down the car will run 10 min more.

a)in terms of x how far can I drive on one tank, b) whats the longest distance I can drive on one tank of gas, c) how fast must I drive in order to go the distance found in b)

so for a) I set up 2 equations 60+x = 300-10x x being miles per hour speed up. and 60-x =300+10x so I solved for x and got x= 240/11 and x=-240/11 from these 2 I get the y-intercept of the parabola. so now I'm trying to find the longest distance I can go in b) and that's the avg of both x values which is 0 so is the longest distance I can go 300 miles?

for c) since 300 miles is achieved by going at 60 mph with a full tank is c) 60?

how can you make a graph of x with this information?

I don't have the answer booklet so I can't really know that answer.

i thank you in advanced for your help

aarbee
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allan
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  • You need to convert 10 mins into hours. – aarbee May 27 '21 at 05:34
  • Suppose you speed up $x$ miles per hour from $60$ mph. This means you're travelling at $x+60$ miles per hour and your car will run for $50-\frac{x}{6}$ hours. now set $D(x)=(x+60)(50-\frac{x}{6})$. This is how car you can drive on one tank. To find the longest distance, maximize $D$ – Matthew H. May 27 '21 at 05:56
  • Should be $(5-x/6)$ instead of $(50-x/6)$ – Michael Hoppe May 27 '21 at 10:03
  • As the distance is $(x+60)(5-x/6)$ with zeroes $-60$ and $30$ you'll find the maximum is at $x=-15$ which gives you a moderate velocity of $45$ mph. – Michael Hoppe May 27 '21 at 15:08

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