Question

Cantina drives home to noise at an average speed of 65 miles per hour and dabney drives home to Portland at an average speed of 50 miles per hour. If the sum of their driving times is 11.3 hours and if the sum of the distances driven is 670 miles, determine the time each woman spent driving home.

Answer 1

Cantina's speed: 65 mph

Dabney's speed: 50 mph

Let's assume

x = Cantina's time

y = Dabney's time

x + y = 11.3 h (1)

and if distance = speed * time

65x + 50y = 670 miles (2)

Now we are gonna solve x on eq. 1.

x = 11.3 - y and we replace this on eq 2.

65(11.3 - y) + 50y = 670

734.5 - 65y + 50y = 670

734.5 - 15y = 670

-15y = -64.5

y = 4.3 hours (Dabney's time)

Finally we replace y - value on eq 1.

x + 4.3 = 11.3

x = 7 hours (Cantina's time)