A car can travel 476 miles on 14 gallons of gas. How do you write equation relating the distance d to the number of gallons g. How many gallons of gas does this car need to travel 578 miles?

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Answer 1 · 2017-05-24T01:21:34

$17" gallons"$

You are given that traveling $476$ miles consumes $14$ gallons of gas. You can rewrite this as a formula:

$476xxd=14xxg$

You can divide both sides by $14$ to get

$476/14 d=1xxg$

$34xxd= 1xxg$

That is, $1$ gallon will take you $34$ miles (or $34$ mpg)

This gives us a conversion factor which can be expressed in one of two ways:

Either $(34" miles")/(1" gallon")$ or $(1" gallon")/(34" miles")$

If you are given gallons, use the first one. If you are given miles, use the second one. You are given miles, so

$578cancel(" miles")xx(1" gallon")/(34cancel(" miles"))=17" gallons"$