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A car travels 20 mph slower in a bad rain storm than in sunny weather. the car travels the same distance in 2 hrs in sunny weather as it does in 3 hrs in rainy weather. find the speed of the car in sunny weather. PLEASE SHOW YOUR WORK.

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iGreen
You can create two equations.

"A car travels 20 mph slower in a bad rain storm than in sunny weather."

[tex]\sf x-20=y[/tex]

Where 'x' represents speed in sunny weather and 'y' represents speed in rainy weather.

"The car travels the same distance in 2 hrs in sunny weather as it does in 3 hrs in rainy weather."

[tex]\sf 2x=3y[/tex]

Where 'x' represents speed in sunny weather and 'y' represents speed in rainy weather.

We want to find the speed of the car in sunny weather, or 'x'. Plug in the value for 'y' in the first equation into the second equation.

[tex]\sf \boxed{\sf x-20}=y[/tex]
[tex]\sf 2x=3y\rightarrow2x=3(x-20)[/tex]

Distribute:

[tex]\sf 2x=3x-60[/tex]

Subtract 3x to both sides:

[tex]\sf -x=-60[/tex]

Divide -1 to both sides:

[tex]\sf x=60[/tex]

So the car goes 60 mph in sunny weather.

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