Question

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?

Answer 1

250 miles

Explanation:

According to the question, 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 and we are now asked to know how far the car could travel on 10 gallons of fuel at 60 mph.

----Distance is inversely proportional to the speed of the car

D = k/s

Where k is the constant

D = distance and S = speed

For every 10 gallons of fuel,the car travels at a speed of 50mph and a distance of 300 miles

300 =k/50

K = 1500

And we are now asked to find the distance of the car if the speed is 60mph

D = k/s

D = 1500/60

D = 250 miles

Answer 2

2500 miles

Explanation:

Since the distance of the car varies inversely with its speed, the distance can be expressed as follows:

`d = (g*a)/(s)` (1)

Where:

d: is the distance

s: is the speed of the car

g: is the gallons of fuel

a: is a constant of proportionality

With the first values, we can find the constant a.

We have:

d = 300 milles

s = 50 mph

g = 10 gallons

Hence, a is:

`a = (d*s)/(g) = (300 m*500 m/h)/(10 g) = 15000 m^(2)g^(-1)h^(-1)`

Now, we can find the distance that the car can travel on 10 gallons of fuel at 60 mph:

`d = (g*a)/(s) = (10 g*15000 m^(2)g^(-1)h^(-1))/(60 m/h) = 2500 m`

Therefore, the car can travel 2500 miles on 10 gallons of fuel at 60 mph.

I hope it helps you!