Alice travels 3 times faster than brenda. traveling in opposite directions, they are 720 miles apart after 7.5 hours. find their rates of travel.

You can solve this by setting up 2 equations

if alice is traveling 3 times faster than brenda, we can make an equation
 
3x=y        x is brenda, y is alice

then we can set up an equation  based on d=rt

720= (x + y)  x 7.5

we can plug in the 1st equation to have the same 2 variables, so for x we can plug in 1/3y or for y we can plug in 3x

720 = (x + 3x) x 7.5

720= 4x x 7.5           divide by 7.5 

96 = 4x         divide by 4

x= 24

brenda is traveling at 24 miles per hour. We can find alice's speed by plugging x back into the 1st equation

3x = y

3(24)= 72

Alice is going 72 miles per hour

Thanks for making the question, I had to remember how to do this

Step-by-step explanation:

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