Answer:
<u>The speed of the first 90 miles was 60 mph and the speed of the last 60 miles was 40 mph. </u>
Step-by-step explanation:
1. Let's review the information given to us to answer the problem correctly:
Distance of the trip = 150 miles
Speed of the first 90 miles of the trip = x
Speed of the last 60 miles of the trip = x - 20
Time of the trip = 3 hours
2. Find their average rate of speed during the last 60 miles.
Let's recall that the formula of speed is:
Speed = Distance/Time, therefore Time = Distance/Speed
Now, we can write our equation to solve for x, this way:
90/x + 60/(x - 20) = 3
90/x = Time of the first 90 miles and 60/(x - 20) = Time of the last 60 miles
90 (x -20 ) + 60x = 3x (x - 20) Lowest Common Denominator = x * (x -20)
90x - 1,800 + 60x = 3x² - 60x
3x² - 210x + 1,800 = 0
x² - 70x + 600 = 0 (Dividing by 3 at both sides)
Using the quadratic formula we have:
x = [- (-70) +/+ √(-70²) - 4 * 1 * 600]/2 * 1
x = [ 70 +/+ √4,900 -2,400]/2
x = [ 70 +/+ 50]/2 √2,500 = 50)
x₁ = (70 + 50)/2 = 120/2 = 60
x₂ = (70 - 50)/2 = 20/2 = 10
<u>We select X₁ that is the one that matches with our problem and therefore, the first 90 miles were driven at 60 mph and the last 60 miles at 40 mph (x - 20). </u>
