Saul drove his truck for 3 hours from Dallas toward Kansas City, then stopped at a truck stop to get dinner. At the truck stop he met Erwin, who had driven for 4 hours from Kansas City toward Dallas. The distance between Dallas and Kansas City is 542 miles and Erwin’s speed was 8 miles per hour slower than Saul’s speed. Find the speed of the two truckers.

Assume that the distance that Saul drove his truck for 3 hours from Dallas toward Kansas City, up to the truck stop where he stopped to get dinner was x.

Then Erwin had driven 542 miles - x.

Using the speed equation, speed = distance / time, you can set the following equations:

Saul' s speed = x / 3 ( in miles per hour)

Erwin's speed = (542 - x) / 4 (in miles per hour)

Erwin’s speed was 8 miles per hour slower than Saul’s speed, hence:

x/3 - (542 - x)/4 = 8 (miles per hour)

Now you can solve the equation (omitting the units)

1. Mutiply both sides by the least common denominator (3 × 4 = 12):

4x - 3 (542 - x) = 96

2. Distributive property:

4x - 1,626 + 3x = 96

3. Add like terms:

7x - 1,626 = 96

4. Add 1,626 to both sides:

7x = 1,722

5. Divide both sides by 7:

x = 246 miles

Then, Saul's speed is x / 3 = 246 miles / 3 hours = 82 miles per hour.

And Erwin' speed is 8 miles per hour less: 82 - 8 = 74 miles per hour.