Question

Driving During a Snowstorm Claire and Chris were driving to their home in Milwaukee when they came upon a snowstorm. They drove at an average rate of 20 miles per hour slower for the last 60 miles during the snowstorm than they drove for the first 90 miles. Find their average rate of speed during the last 60 miles if the trip took 3 hours.

I know the answer is "40 mph" BUT I don't know how to show the work because this problem is hard so please help me. Thank you

Answer 1

The speed of the first 90 miles was 60 mph and the speed of the last 60 miles was 40 mph.

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

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).