The bike can go for 660 miles with a full tank of gas. The direct variation method is used for solving this kind of word problem.
<h3>What is the direct variation method?</h3>
The direct variation method is used for solving word problems that have directly proportionated events.
Consider x1, x2 as inputs and y1, y2 as outputs of an event.
So, the proportionality between them is mentioned as
y1: x1 = y2: x2
Then we can write it as
y1/x1 = y2/x2
The general form of the direct variation is y = kx; where y is the output of the event, x is the input of the event and k is the constant.
<h3>Calculation:</h3>
It is given that,
A motorcycle drove 178 miles on 3 gallons of gas.
So, x1 = 3; y1 = 178; x2 = 10;
Then, for 10 gallons of gas, the bike drives for y2 miles.
So,
y1/x1 = y2/x2
⇒ 178/3 = y2/10
⇒ 66 = y2/10
⇒ y2 = 66 × 10
∴ y2 = 660 miles.
Thus, with 10 gallons of gas, the bike can go for 660 miles.
Learn more about the direct variation method here:
brainly.com/question/10617012
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