Cabrina and Dabney are attending a conference. After the conference, Cabrina drives home to Boise at an average speed of 7575 miles per hour and Dabney drives home to Portland at an average speed of 6060 miles per hour. If the sum of their driving times is 11.511.5 hours and if the sum of the distances driven is 765765 miles, determine the time each woman spent driving home.

Cabrina's time = 5 hours  

Dabney's time = 6.5 hours

Step-by-step explanation:

The data of the exercise are:

Cabrina speed = 75 mph

Daney speed = 60 mph

The sum of their distance is 765 miles, therefore

Cabrina's distance Dabney's distance = 765

Cabrina's distance = x

Dabney's distance = 765-x

The sum of their times is 11.5 hours, therefore

Cabrina's time Dabneys time = 11.5

Cabrina's time = x / 75

Dabney's time = (765-x) / 60

x / 75 (765-x) / 60 = 11.5

Lowest common denominator of 75 and 60 is 300, therefore we have:

330 * x / 75 300 * (765-x) / 60 = 300 * 11.5

4 * x 5 * (- x 765) = 3450

4 * x - 5 * x 3825 = 3450

x = 375

Replacing:

Cabrina's time = 375/75 = 5 hours took

Dabney's time = (765-375) / 60 = 6.5 hours took

Step-by-step explanation:

Below is an attachment containing the solution.

attachment?

step-by-step explanation: