Question

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.

Answer 1

Alice travels 3 times faster than Brenda. To find their rates of travel, we can set up an equation using the distance formula and solve for Brenda's rate of travel. Brenda's rate of travel is 6 mph and Alice's rate of travel is 18 mph.

Step-by-step explanation:

In this problem, Alice and Brenda are traveling in opposite directions and are 720 miles apart after 7.5 hours. We need to find their rates of travel. Let's assume Brenda's rate of travel is x mph, then Alice's rate of travel will be 3x mph since Alice travels 3 times faster than Brenda.

To find their rates of travel, we can use the formula: Distance = Rate x Time.

Since they are 720 miles apart and have traveled for 7.5 hours, we can set up the equation 720 = (x + 3x) * 7.5.

Simplifying the equation, we get 720 = 4x * 7.5. Dividing both sides by 30 gives us x = 6.

Therefore, Brenda's rate of travel is 6 mph and Alice's rate of travel is 3x, which is -

= 3 * 6 = 18 mph.

Answer 2

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