The distance between Caroline's house and Laura's house is 3120m Carolina and Laura leave their house at the same time the two girls cycle towards each other until they meet Caroline speed is 7.2 meters per second and Laura Speed is 8.4 meters per second a how long do the girls have to ride before they need be what is the distance between Caroline's house and where the girls meet show all your work you do to arrive at your solution and explain your reasoning
total distance covered per second
= 7.2 + 8.4 = 15.6 meters/s
time = 3120/15.6 seconds to collision
That is all you need.
To solve this problem, we can use the formula:
Distance = Speed x Time
Let's assume that the time it takes for Caroline and Laura to meet is 't' seconds.
Caroline's speed is given as 7.2 meters per second, so the distance she covers in 't' seconds is 7.2t meters.
Laura's speed is given as 8.4 meters per second, so the distance she covers in 't' seconds is 8.4t meters.
When the two girls meet, the sum of the distances they covered will be equal to the total distance between their houses, which is 3120 meters.
So we have the equation: 7.2t + 8.4t = 3120.
Combining like terms, we get 15.6t = 3120.
Dividing both sides by 15.6, we find t = 200.
Therefore, the girls need to ride for 200 seconds before they meet.
To find the distance between Caroline's house and where the girls meet, we can substitute the value of 't' into either equation:
Distance = 7.2t = 7.2 x 200 = 1440 meters.
Therefore, the distance between Caroline's house and where the girls meet is 1440 meters.
To find out how long the girls need to ride before they meet and the distance between Caroline's house and where they meet, we can use the formula:
Time = Distance / Speed
Let's calculate the time it takes for both Caroline and Laura to meet. Since they are cycling towards each other, we can add their speeds.
Caroline's speed = 7.2 m/s
Laura's speed = 8.4 m/s
Their combined speed is 7.2 m/s + 8.4 m/s = 15.6 m/s.
To calculate the time, we use the formula:
Time = Distance / Speed
Distance between the houses = 3120 m
Combined speed = 15.6 m/s
Time = 3120 m / 15.6 m/s
By dividing 3120 by 15.6, we find that it takes 200 seconds for Caroline and Laura to meet.
Now, let's find the distance between Caroline's house and where they meet. We can multiply the speed by the time:
Distance = Speed * Time
Distance = 7.2 m/s * 200 s
By multiplying 7.2 by 200, we find that the distance between Caroline's house and where they meet is 1440 meters.
Therefore, the girls need to ride for 200 seconds, and the distance between Caroline's house and where they meet is 1440 meters.