a bicycle rider left town at noon at traveled at a uniform rate of 15 miles an hour. at 2 pm the same day, a motorcycle rider left for the same place at a uniform rate 30 miles an hour higher. at what time did the motorcycle rider overtake the bicycle rider?
An agate terrifies.
To find out at what time the motorcycle rider overtook the bicycle rider, we can use the concept of relative speed.
Let's consider the time it takes for the motorcycle rider to catch up to the bicycle rider as 't' hours.
In the 2 hours between noon and 2 pm (when the motorcycle rider started), the bicycle rider had already been traveling for 2 hours at a speed of 15 miles per hour, which means the bicycle rider had covered a distance of 2 * 15 = 30 miles.
Now, let's set up an equation to represent the relative speed between the bicycle rider and the motorcycle rider:
Relative Speed = Speed of Motorcycle - Speed of Bicycle
Since the motorcycle rider is traveling 30 miles/hour faster than the bicycle rider, the relative speed can be written as:
Relative Speed = 30 miles/hour
We also know that the distance between the motorcycle rider and the bicycle rider is initially 30 miles because the bicycle rider was 30 miles ahead when the motorcycle rider started.
Distance = Relative Speed * Time
30 miles = 30 miles/hour * t hours
Simplifying the equation:
30 = 30t
Dividing both sides of the equation by 30:
t = 1 hour
Therefore, it will take 1 hour for the motorcycle rider to catch up to the bicycle rider.
Since the motorcycle rider started at 2 pm, we add the time it takes (1 hour) to find out when the motorcycle rider will overtake the bicycle rider.
2 pm + 1 hour = 3 pm
The motorcycle rider will overtake the bicycle rider at 3 pm.
To determine the time at which the motorcycle rider overtakes the bicycle rider, we need to find out their relative distance.
Let's assume the time it takes for the motorcycle rider to catch up to the bicycle rider is "t" hours after 2 pm. Since the bicycle rider left town at noon (12 pm), they had a 2-hour head start on the motorcycle rider.
The distance traveled by the bicycle rider in t hours is given by:
Distance = Speed × Time
Distance = 15 × t
The distance traveled by the motorcycle rider in t hours is given by:
Distance = Speed × Time
Distance = (15 + 30) × t [Since the motorcycle rider is traveling 30 miles per hour faster]
For the motorcycle rider to catch up to the bicycle rider, their distances should be equal:
15 × t = (15 + 30) × t
Let's solve this equation to find the value of "t":
15t = 45t
45t - 15t = 0
30t = 0
t = 0
The value of "t" is zero, which means the motorcycle rider overtakes the bicycle rider immediately after 2 pm. Therefore, the motorcycle rider overtakes the bicycle rider at exactly 2 pm.
Thus, the answer is that the motorcycle rider overtakes the bicycle rider at 2 pm.