Question: kara and steven are biking around a 1,800 kilometer path. they start biking from the same place, at the same time, and in the same direction. kara bikes at a speed of 15 km/h and steven bikes at a speed of 30 km/h. how long will it take before steven and kara will be at the same place of the path next time?

120 hours



Explanation:

The path is 1800 km. Kara's speed is 15 km/h. If this speed is held the same throughout the path, then it will take her d/r = 1800/15 = 120 hours to travel the entire path until she gets back to her starting point.

For Steven, it takes him d/r = 1800/30 = 60 hours to make the same journey.

The LCM of 60 and 120 is 120

Every 120 hours, both Kara and Steven will be back at the starting point together. 

Note: this is a very very large time value, and this is not considering the fact that the bikers slow down or stop to take a break.