A certain truck uses 1/12 + kv^2 gallons

A certain truck uses 1/12 + kv^2 gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses 5/12 gallon of fuel per mile?

1 Explanation

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Zubin Baisiwala

I did not understand the solution of og for this question.
We need to calculate average speed truck travels so that it uses 5/12 gallon of fuel per mile.
Option one gives value of k. Even if we plug value of k in 1/12 +kv^2, why would we equate this with 5/12? How can we assume that v miles per hour is constant and equation is equal to 5/12?
Option two gives us speed of 30 m/hr and uses 1/6 gallon per mile. How can we plug these values in 1/12 + kv^2 and equate with 1/6?

Is it that in both cases 1/12+kv^2 is equation for any gallon of fuel per mile travelling at v miles per hour?
Please help me clear this

Nov 29, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Zubin :)

Happy to help! The question in the prompt reads:

"At what speed should the truck travel so that it uses 5/12 gallon of fuel per mile?"

And we're also given the equation:

[gallons of fuel/mile] = 1/12+kv^2

When we plug in the value of gallons of fuel per mile into the equation, we see that we have two unknowns: k and v.

5/12 = 1/12+kv^2

If we know k, then we can solve for v and therefore answer the question in the prompt. Since we're considering one specific truck, the value of k will be the same regardless of the speed traveled.

Let's look at statement 1: The value of k is 1/10800.

Plugging this value into the equation above, we get

5/12 = 1/12+(1/10800)v^2

Notice how we have 1 equation with 1 variable (v, the speed we want to calculate). This shows us that we can answer the question in the prompt given statement 1.

Statement 2 reads: When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.

Working with this statement is a little trickier, since we're not directly given a value for k, and we're also looking at a different value for the left side of the equation. The speed, v, is 30 mi/hr:

1/6 = 1/6 + k*30

Now, at this point, we could solve the for value of k for the truck. And once we have k, we can plug that value into the equation

5/12 = 1/12+kv^2

to find the speed of the truck at which it uses 5/12 gallons/mi.

Again, k is a constant in this situation that is independent of the speed of the truck. If we can find k, then we can use that value to find the speed at which the truck uses 5/12 gallons/mi. This is exactly what we do with statement 2.

I hope this helps :)

Dec 9, 2016 • Reply