Jason and Britton are driving to St. George. Jason got a 20 mile head start and drove an
1 answer:
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.
__
<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 might be interested in
Answer/Step-by-step explanation:
a. Using a point on the graph, (6, 12), and the slope of the line, we can first generate an equation in the point-slope form, given as , where,
m = slope, and (a, b) is a point on the line.
Using two points, (6, 12) and (3, 21), let's find slope, m.
Using a point (6, 12) and slope, m = -3, generate an equation in the point-slope form by substituting a = 6, b = 12, and m = -3 in .
✅Equation in point-slope form would be:
Rewrite this to make it be in the slope-intercept form, .
Add 12 to both sides
✅The equation in slope-intercept form is
b. ✍️Based on the linear model, , the 30 represents b = y-intercept.
✅Therefore, it took Peter 30 mins long initially to deliver his package.
✍️Based on the linear model, , "-3" represents the slope.
✅Therefore, Peter's delivery time decreased 3 mins per day.