A semi-truck travels on a paved road for 2 hours at an average speed of 20 miles per hour faster than it travels on a dirt road. The time spent on the dirt road is 3 hours. If the entire trip is 200 miles, how fast is the truck traveling on the dirt road?

Use d = r * t for both the paved and the dirt roads. Use x for the unknown speed on the dirt road.

For the paved road, use d1 (distance 1):
d1 = r * t
d1 = (x + 20) * 3
so
d1 = 3(x + 20)

For the dirt road, use d2 (distance 2):
d2 = r * t
d2 = x * 3
so
d2 = 3x

Also, you know that the distance traveled on the paved road, d1, and the distance traveled on the dirt road, d2, sum to 200 miles. Thus, you know:
d1 + d2 = 200

See if you can take it from there.

To determine the speed of the truck on the dirt road, we can first determine the speed on the paved road.

Let's assume the speed on the dirt road is 'x' miles per hour.

According to the given information, the truck spends 2 hours on the paved road, traveling at an average speed of 20 miles per hour faster than the dirt road. Therefore, the speed on the paved road can be calculated as 'x + 20' miles per hour.

Using the formula: Speed = Distance/Time, we can calculate the distance covered on each road.

Distance on the paved road = (x + 20) miles per hour * 2 hours = 2x + 40 miles.
Distance on the dirt road = x miles per hour * 3 hours = 3x miles.

The total distance covered in the entire trip is given as 200 miles. Therefore, the sum of the distances on the paved and dirt roads should equal 200 miles.

2x + 40 + 3x = 200

Simplifying the equation, we get:

5x + 40 = 200
5x = 200 - 40
5x = 160
x = 32

So, the speed of the truck on the dirt road is 32 miles per hour.