Question

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.

Answer 1

Answer:

Speed of Sharon on country roads = 50 mph

Step-by-step explanation:

Let the speed of Sharon on interstate roads was = a mph

And the speed on country roads = b mph

Time taken by Sharon to travel 390 miles on interstate = $\frac{\text{Distance}}{\text{Speed}}$

= $\frac{390}{a}$ hours

Time taken by Sharon to travel 150 miles on country roads = $\frac{150}{b}$ hours

"Total time for the trip = 9 hours"

$\frac{390}{a}+\frac{150}{b}=9$

$\frac{130}{a}+\frac{50}{b}=3$ --------(1)

"Her speed on interstate was 15 mph more than on country roads".

a = b + 15 ---------(2)

By substituting the value of a from equation (2) to equation (1),

$\frac{130}{(b+15)}+\frac{50}{b}=3$

$\frac{130b+50(b+15)}{b(b+15)}=3$

180b + 750 = 3b(b + 15)

180b + 750 = 3b² + 45b

3b² + 45b - 180b - 750 = 0

3b² - 135b - 750 = 0

b² - 45b - 250 = 0

b² - 50b + 5b - 250 = 0

b(b - 50) + 5(b - 50) = 0

(b + 5)(b - 50) = 0

b = -5, 50

But the speed can't be negative,

Therefore, b = 50 mph

Speed of Sharon on country roads was 50 mph.