Two cyclists start out on the same trail together that is overall 20km long. The first cyclist completes the entire trail and is traveling at a constant 20 km/hr for the away part of the trip and then only 15 km/hr for the return trip. the Second cyclist, who is slower, is moving along at a Constant 10 km/hr for the entire trip. The second cyclist wants to turn around at some point so that he will arrive back at the starting position at the same time that the first cyclist will arive. At what point along the path should he do that?
cyclist 1
1 hour out
20/15 = 4/3 hour back
total time = 7/3 hour
so the second wants to go out for (1/2)(7/3) hours = 7/6 hour at 10 km/hr
70/6 = 11 2/3 kilometer
To find the point at which the second cyclist should turn around, we need to determine the time it takes for both cyclists to complete their trips. Since the first cyclist completes the entire 20km trail, let's calculate the time it takes for him to do so.
First cyclist (faster one):
For the away part of the trip:
Distance = Speed × Time
20km = 20km/hr × Time
Time = 1 hour
For the return part of the trip:
Distance = Speed × Time
20km = 15km/hr × Time
Time = 4/3 hours (or 1 hour and 20 minutes)
Total Time taken by the first cyclist = Time for away part + Time for return part
Total Time = 1 hour + 4/3 hours = 7/3 hours
Now, let's calculate the time taken by the second cyclist.
Second cyclist (slower one):
Distance = Speed × Time
20km = (10km/hr × Time) + (10km/hr × Time)
20km = 20km/hr × Time
Time = 1 hour
Since both cyclists should arrive back at the starting position at the same time, the second cyclist needs to turn around after 1 hour of cycling. This means he should turn around halfway through the trip, which is at the 10km mark.
Therefore, the second cyclist should turn around at the 10km point on the trail in order to arrive back at the starting position at the same time as the first cyclist.