# During rush hour, Fernando can drive 20 miles using the side roads in the same time that it takes to travel 15 miles on the freeway. If Fernando's rate on the side roads is 9 mi/h faster than his rate on the freeway, find his rate on the side roads. What is the formula and what do I use where.

Time in each case is the same.

distance=rate*time

20=(9+vf)*time

where vf is the velocity on the freeway.

15=vt*time or time= 15/vf

put that in the first equation for time, and solve for vf. You will most likely have a quadratic equation.

## To find Fernando's rate on the side roads, let's start by setting up the equations:

Let's assume Fernando's rate on the freeway is vf miles per hour.

So, his rate on the side roads would be (vf + 9) miles per hour.

Now, let's use the formula distance = rate * time to set up the equation for each scenario:

On the side roads: distance = 20 miles, rate = (vf + 9) miles per hour

20 = (vf + 9) * time

On the freeway: distance = 15 miles, rate = vf miles per hour

15 = vf * time

Since we are told that the time is the same in both scenarios, we can equate the two equations:

(vf + 9) * time = vf * time

Now, let's solve for the rate on the side roads (vf + 9):

Divide both sides of the equation by time:

vf + 9 = vf

Subtract vf from both sides:

9 = 0

This leads to a contradiction, which means there is no solution for the rate on the side roads. However, this cannot be true since we are given that Fernando can drive 20 miles on the side roads in the same time it takes to travel 15 miles on the freeway.

Therefore, there may be an error or inconsistency in the given information or calculations. Please double-check the problem statement and equations provided.