a 360 mile trip began on a greeway in a car traveling at 62 mph. Once the road became a 2 lane highway, the car slowed to 54 mph. If the total trip took 6 hours, find the time spent on each type of road

Time spent on the greenway road = 4.5 hours

Time spent on the 2 lane road = 1.5 hours

Explanation:

The distance of the trip is 360 miles and the initial speed of the car is 62 miles/hr and after the road became 2 lane highway the car slowed to 54 miles/hr.

Let us divide the trip into two

Greenway

speed = distance/time

speed = 62 mph

time = a

distance = speed * time

distance = 62a

2 lane highway

speed = distance/time

speed = 54 mph

time = b

distance = speed * time

distance = 54b

Total distance

62a + 54b = 360 ... (i)

Total time

a + b = 6 ... (ii)

a = 6-b

insert a in equation (i)

62 (6-b) + 54b = 360

372 - 62b + 54b = 360

-8b = 360-372

-8b = - 12

b = 12/8

b = 1.5

from equation (ii)

a + 1.5 = 6

a = 6 - 1.5

a = 4.5