Help please this i will mark brainliest please
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Answer:
2 hours, 150 miles
Step-by-step explanation:
The relation between time, speed, and distance can be used to solve this problem. It can work well to consider just the distance between the drivers, and the speed at which that is changing.
<h3>Separation distance</h3>Jason got a head start of 20 miles, so that is the initial separation between the two drivers.
<h3>Closure speed</h3>Jason is driving 10 mph faster than Britton, so is closing the initial separation gap at that rate.
<h3>Closure time</h3>The relevant relation is ...
time = distance/speed
Then the time it takes to reduce the separation distance to zero is ...
closure time = separation distance / closure speed = 20 mi / (10 mi/h)
closure time = 2 h
Britton will catch up to Jason after 2 hours. In that time, Britton will have driven (2 h)(75 mi/h) = 150 miles.
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<em>Additional comment</em>
The attached graph shows the distance driven as a function of time from when Britton started. The distances will be equal after 2 hours, meaning the drivers are in the same place, 150 miles from their starting spot.
You haven't provided the coordinates of C and D, therefore, I cannot provide an exact solution. However, I'll tell you how to solve this problem and you can apply on the coordinates you have.
The general form of the linear equation is:
y = mx + c
where:
m is the slope and c is the y-intercept
1- getting the slope:
We will start by getting the slope of CD using the formula:
slope = (y2-y1) / (x2-x1)
We know that the line we are looking for is perpendicular to CD. This meas that the product of their slopes is -1. Knowing this, and having calculated the slope of CD, we can simply get the slope of our line
2- getting the y-intercept:
To get the y-intercept, we will need a point that belongs to the line.
We know that our line passes through the midpoint of CD.
Therefore, we will first need to get the midpoint:
midpoint = (
)
Now, we will use this point along with the slope we have to substitute in the general equation and solve for c.
By this, we would have our equation in the form of:
y = mx + c
Hope this helps :)
The general form of the linear equation is:
y = mx + c
where:
m is the slope and c is the y-intercept
1- getting the slope:
We will start by getting the slope of CD using the formula:
slope = (y2-y1) / (x2-x1)
We know that the line we are looking for is perpendicular to CD. This meas that the product of their slopes is -1. Knowing this, and having calculated the slope of CD, we can simply get the slope of our line
2- getting the y-intercept:
To get the y-intercept, we will need a point that belongs to the line.
We know that our line passes through the midpoint of CD.
Therefore, we will first need to get the midpoint:
midpoint = (
Now, we will use this point along with the slope we have to substitute in the general equation and solve for c.
By this, we would have our equation in the form of:
y = mx + c
Hope this helps :)