When driving the 9 hour trip home, Sharon drove 390 miles on the interstate and 150 miles on country roads. Her speed on the interstate was 15 mph more than on country roads. What was her speed on country roads? Set up a rational equation and solve.

Speed on country road

X = 46.777miles per hour

Step-by-step explanation:

Total time for travel is 9 hours.

390 miles on interstate

150 miles on country road.

Let country road speed = x

Interstate speed=y

But

X + 15m/h = y

Time on interstate = 390/y

Time on country = 150/x

But y = x+15

Interstate = 390 / (x+15)

Country = 150/x

Adding the two will give us 9 hours

390 / (x+15) + 150/x = 9

9x²-405x-750 = 0

Solving quadratically

X = 46.777miles per hour

Y = 46.777+15 = 61.777 miles per hour