Question

Bruce rents snowmobiles to tourists. He charges $135 for 4 hours and $202.50 for 6 hours? What is the hourly rate Bruce charges to rent a snowmobile? Write a direct variation equation, then solve.

Answer 1

Answer: Hourly rate of rent a snowmobile is $ 33.75.

Explanation:

Since we have given that

Amount Bruce charges for 4 hours = $135

Amount Bruce charges for 6 hours = $ 202.50

Since there is direct variation, as with the increase in hours the cost will also increase.

So, it will be written like this :

`(135)/(4)=(202.5)/(6)`

But we need to find the hourly rate which will be

`(135)/(4)=\$33.75`

Hence, hourly rate of rent a snowmobile is $ 33.75.

Answer 2

The hourly rate Bruce charges is, $33.75

Explanation:

Direct Variation states two variables that can be expressed by an equation in which one variable is equal to a constant times the other, or we can say that if one variable changes then the other changes in proportion to the other.

i.e
`y \propto x` or

y = kx where k is the constant.

Let x be the number of hours and y be the charges.

He charges $ 135 for 4 hours, by using direct variation;

⇒
`135= k( 4)`

Solve for k:

`k = (135)/(4) = \$ 33.75` per hour

Now, for 6 hours he charges $ 202.50, by using direct variation.

⇒
`202.50 = k(6)`

Now, solve for above k: we have

`k = (202.50)/(6)  = \$ 33.75` per hour.

Therefore, the hourly rate Bruce charges to rent a snowmobile, k is, $ 33.75