Michael drove to the mountains last weekend. there was heavy traffic on the way there at the trip took six hours. when michael drove home there was no traffic and the trip only took four hours. if his average rate was 22 mph faster on the trip home how far away does michael live from the mountains?

264 Miles

Step-by-step explanation:

Let's imagine that going to the mountains she traveled at x miles per hour.  Then according to the problem, on the way home, without traffic, she traveled at x + 22 miles per hour.

We know that the distance is the same in each direction.  

If she traveled at speed x for 6 hours going to the mountains, the distance she traveled was 6x.

Coming home she traveled at speed (x + 22) for 4 hours, or 4(x + 22).

But since the distance is the same each way, we can say

6x = 4(x + 22)

Now we can just manipulate the equation to solve for x.

6x = 4x + 88

2x = 88

x = 44.

If x = 44, then her trip to the mountains we 6 hours times 44 miles per hour, or 264 miles.

(https://www.wyzant.com/resources/answers/91993/martina_drove_to_the_mountains_last_weekend_there_was_heavy_traffic_on_the_way_there_and_the_trip_took_6_hours_when_martina_drove_home_there_was_no_traff)

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

step-by-step explanation: