.Due to wind resistance, a car's gas mileage is inversely proportional to the square of its highway driving speed. A particular car gets 32 miles per gallon at a highway driving speed of 65mph. What gas mileage would it get for a highway driving speed of 75mph?

Question

kl0723 · Answer

lets x be the car's mileage at at certain speed... if x is inversely proportional to the square of the highway driving speed, then $$x=\frac{ n }{ (s)^2 }$$

kl0723 · Answer

s= speed

anonymous · Answer

so $$32mph = 1\div 65^2 mph$$

kl0723 · Answer

$$32=\frac{ n }{ (65)^2 }$$

kl0723 · Answer

lets solve for n... $$n=(65)^2*(32)\
\[n=135,200$$

kl0723 · Answer

disregard the red thing xD I hate this equation builder

anonymous · Answer

lol okay, now whats the next step?

kl0723 · Answer

lets use the n value to solve for x, when s=75 mph...
$$x=\frac{ n }{ (75)^2 }$$

kl0723 · Answer

$$x=\frac{ (135,200) }{ (75)^2 }=$$

kl0723 · Answer

24 mpg

anonymous · Answer

so the mpg would be less for 75mph than 65?

kl0723 · Answer

they're inversely proportional... when the speed goes up the mpg's go down, plus you have to take into account more air resistance and also engine revolution increments

kl0723 · Answer

seems reasonable I guess

anonymous · Answer

Could you help me with this problem now? 
(The intensity of light varies inversely as the square of the distance from the light source. A car approaches John's parked car from the opposite direction with its bright lights on. How much more intense is the light when the cars are 20 feet apart than if it was when they were 100 feet apart?

anonymous · Answer

thanks for all your help by the way!

kl0723 · Answer

this is basically the same thing :P brightness is inversely proportional to distance

anonymous · Answer

so the light is 5xs more intense when 20 ft away than when 100ft away.