2 cyclists start at the same tiem from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and the second is riding at 16mph. How long after they begin will they meet?
The distance between them decreases at a rate 16 + 14 = 30 mph.
How long before the 45 mile separation gets reduced to 0?
45/30 = ? hours
To find out when the two cyclists will meet, we can use the concept of relative speed. Since they are moving towards each other, we can add their speeds to calculate the relative speed.
The cyclist riding at 14 mph will travel a distance of 14t miles, where t is the time in hours.
The cyclist riding at 16 mph will travel a distance of 16t miles.
Since the total distance between them is 45 miles, we can set up the equation:
14t + 16t = 45
Combine like terms:
30t = 45
Divide both sides of the equation by 30:
t = 45 / 30
Simplifying:
t = 1.5 hours
Therefore, they will meet after 1.5 hours since they began.
To find out when the two cyclists will meet, we can use the formula:
Time = Distance / Speed
Let's denote the time it takes for them to meet as "t". Since they start at the same time, cyclist 1 and cyclist 2 will meet each other in t hours.
The distance cyclist 1 travels in t hours is 14t miles, and the distance cyclist 2 travels in t hours is 16t miles. Since they meet at the middle of the course, the total distance covered by both cyclists should add up to the total length of the course, which is 45 miles.
So, we can set up an equation:
14t + 16t = 45
Combining the like terms:
30t = 45
Now, divide both sides of the equation by 30 to solve for t:
t = 45 / 30
t = 1.5
Therefore, it will take them 1.5 hours to meet after they begin.