Romeo and Juliet first saw each other when they were 270 feet apart. Romeo began running toward Juliet at a rate of 16 ft/s. At the same moment, Juliet began running toward Romeo at a rate of 14ft?s.
A. How many seconds after they started running will they meet?
B. How far will Romeo have run then?
To solve this problem, we can use the concept of relative speed. The relative speed between Romeo and Juliet is the sum of their individual speeds.
A. To find out when they will meet, we need to determine the time it takes for the distance between them to become zero.
Let's assume the time taken for them to meet is t seconds.
Initially, they are 270 feet apart.
At time t, Romeo would have covered a distance of 16t feet (since he is running at a rate of 16 ft/s).
Similarly, at time t, Juliet would have covered a distance of 14t feet (since she is running at a rate of 14 ft/s).
Now, to find the time when they meet, we can set up an equation:
270 - (16t + 14t) = 0
Simplifying the equation:
270 - 30t = 0
30t = 270
t = 270 / 30
t = 9 seconds
Therefore, they will meet after 9 seconds.
B. To find out how far Romeo will have run at that time, we can substitute the value of t into Romeo's distance formula:
Distance covered by Romeo= 16t
Distance covered by Romeo= 16 * 9
Distance covered by Romeo= 144 feet
So, Romeo will have run 144 feet when they meet after 9 seconds.
To answer these questions, we can use the concept of relative speed. Relative speed measures the rate at which one object is moving with respect to another object.
A. To find out how many seconds it will take for Romeo and Juliet to meet, we need to calculate their relative speed and divide the initial distance between them by this relative speed.
The relative speed of Romeo and Juliet can be found by adding their individual speeds. So, the relative speed of Romeo and Juliet is 16 ft/s (Romeo's speed) + 14 ft/s (Juliet's speed) = 30 ft/s.
The initial distance between Romeo and Juliet is given as 270 feet. To find out how many seconds it will take for them to meet, we divide the initial distance by the relative speed:
Time = Distance / Speed
Time = 270 ft / 30 ft/s
Time = 9 seconds
Therefore, it will take 9 seconds for Romeo and Juliet to meet.
B. To find out how far Romeo will have run when they meet, we can multiply Romeo's speed by the time it takes for them to meet.
Romeo's speed is 16 ft/s, and the time taken for them to meet is 9 seconds. Multiplying these values, we get:
Distance = Speed × Time
Distance = 16 ft/s × 9 s
Distance = 144 feet
Therefore, Romeo will have run 144 feet when they meet.