Ared car is traveling at 55 mph. a blue car is traveling at 65 mph. the cars are 305 miles apart. the cars started at the same spot at different times. the total driving time for the two cars is 5 hours. which system of equations could be used to solve for the total driving time of the red car (r) and the total driving time of the blue car (b)?

Step-by-step explanation:

let red car travels x hours

and blue car travels y hours

then x+y=5

x=5-y

case 1.

let they move in different directions.

and 65 y+55 x=305

or 13 y+11 x=61

13 y+11 (5-y)=61

13 y+55-11 y=61

2 y=61-55

or 2 y=6

y=3

x=5-3=2

red car travels=2 hours

blue car travels=3 hours.

case 2.

if the travel in the same direction.

65 y-55 x=305

13 y-11 x=61

13 y-11(5-y)=61

13 y-55+11 y=61

24 y=61+55

or 24 y=116

or 6y=29

y=29/6 hours=4 hours 50 minutes.

x=5-29/6=1/6 hours=10 minutes.

so red car travels 10 minutes

and blue car travels 4 hours 50 minutes.