Fred and his good buddy Gabriel are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Fred has already finished 8 oil changes today, and can complete more at a rate of 1 oil change per hour. Gabriel just came on shift, and can finish 3 oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How long will that take? How many oil changes will Fred and Gabriel each have done?

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CorbenW66309id CorbenW66309id · Answer 1

EXPLANATION

Assuming that x represents the number of oil changes hours, the expression will be:

[tex]Fred\longrightarrow8+1x[/tex][tex]Gabriel\longrightarrow0\text{ + 3x}[/tex]

If the friends are tied, and have the same number of oil changes, we can match both equations in order to get the number of hours:

[tex]8+x=3x[/tex]

Subtracting -x to both sides:

[tex]8=3x-x[/tex]

Subtracting like terms:

[tex]8=2x[/tex]

Dividing both sides by 2:

[tex]\frac{8}{2}=x[/tex]

Simplifying:

[tex]4=x[/tex]

Plugging in x=4 into each expression:

[tex]Fred\longrightarrow8+4=12\text{ changes}[/tex][tex]\text{Gabriel }\longrightarrow\text{ 3}\cdot4\text{ }=\text{ 12 changes}[/tex]

In conclusion, in 4 hours, both men will have completed 12 oil changes.