2 cyclists travel opposite on circular trail that is 5 miles long. one cyclist travels 12 miles per hour, the other travels 18 miles per hour. How long before they meet?
Visualize the track laid out in a straight line, then they would meet if the total distance they traveled is 5 miles, of course they both took the same time.
let that time be t
12t + 18t = 5
30t = 5
t = 5/30 = 1/6 hour or 10 minutes.
To find out how long it will take for the two cyclists to meet, we need to determine the relative speed at which they are approaching each other. This can be found by adding their individual speeds together.
In this case, one cyclist is traveling at 12 miles per hour, while the other is traveling at 18 miles per hour. To calculate their relative speed, we add these two speeds together:
Relative Speed = 12 mph + 18 mph = 30 mph
Now that we have the relative speed, we can calculate the time it will take for the cyclists to meet by dividing the distance between them (5 miles) by their relative speed:
Time = Distance / Relative Speed
Time = 5 miles / 30 mph
To simplify the calculation, we can convert the speed from miles per hour to miles per minute by dividing it by 60 (since there are 60 minutes in an hour):
Relative Speed = 30 mph รท 60 = 0.5 miles per minute
Now we can calculate the time it will take for the two cyclists to meet:
Time = 5 miles / 0.5 miles per minute
Time = 10 minutes
Therefore, the two cyclists will meet in 10 minutes.