Two camper vans leave Arrowhead Lake at the same time, one traveling north at a speed of 10 km/h faster than the other, which is traveling south. After 3 hours, the camper vans are 420 km apart. Find their speeds
Let's say the speed of the first camper van (going north) is x km/h.
Then the speed of the second camper van (going south) is x + 10 km/h.
Since they are moving in opposite directions, their combined speed is x km/h + (x + 10) km/h = 2x + 10 km/h.
We know that they are 420 km apart after 3 hours, so the total distance traveled by both camper vans is 420 km.
The total distance traveled is equal to the combined speed multiplied by the time taken:
3 hours * (2x + 10 km/h) = 420 km.
Multiplying out the brackets gives: 6x + 30 km/h = 420 km.
Subtracting 30 km/h from both sides gives: 6x = 390 km.
Dividing both sides by 6 gives: x = 65 km/h.
So the first camper van is traveling at a speed of 65 km/h, and the second camper van is traveling at a speed of x + 10 = 65 + 10 = 75 km/h. Answer: \boxed{65 \text{ km/h}, 75 \text{ km/h}}.