SOLUTION: The distance a car can travel on a certain amount of fuel varies inversely with its speed. If a car traveling 50 mph can travel 300 miles on 10 gallons of fuel, how far could the

Question 42120: The distance a car can travel on a certain amount of fuel varies inversely with its speed. If a car traveling 50 mph can travel 300 miles on 10 gallons of fuel, how far could the car travel on 10 gallons of fuel at 60 mph?
Thank you
Found 2 solutions by fractalier, psbhowmick:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
For an inverse relation such as this we have
d = kf / s
Now plug in to find k
300 = k(10) / 50
k = 1500
Now redo it with the new k
d = 1500f / s
Now plug in the new data to find d
d = 1500(10) / 60
d = 250 miles
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
Let car speed = 'v' mph and distance traveled = 's' miles.
[As the amount of fuel remains constant (= 10 gallons) so it will not come in any equation.]
As distance traveled varies inversely as the speed, so
________(1)
where k = constant of variation.

When v = 50, s = 300.
Put this in eqn.(1).
Thus we get

or k = 15000

So, putting the value of k eqn(1) becomes
________(2)

When v = 60 from (2) we get
= 250

The reqd. distance is 250 miles.
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