Alan leaves los angeles at 8: 00 am to drive to san francisco, 400 mi away. he travels at a steady 50 mph. beth leaves los angeles at 9: 00 am and drives a steady 60 mph. who gets to san francisco first? how long does the first to arrive have to wait for the second?

Given, Alan leaves Los Angeles at 8:00 am to San Fransisco which is 400 miles away from Los Angeles.

He travels at a rate of 50 mph.

So 50 miles distance covered in 1 hour

1 mile distance covered in hour

400 miles distance covered in hours = 8 hours.

Alan takes 8 hours to reach San Fransisco.

The time will be = 8:00 am + 8 hours = 4:00 pm.

Now Beth leaves Los Angeles at 9:00 am.

His speed is 60mph.

So 400 miles distance covered in hours.

We can simplify by dividing 400 and 60 both by 20. We will get there after simplification.

So Beth takes hours to reach San Fransisco.

Let's convert hours to minute. We know that there are 60 minutes in 1 hour.

So hours = minutes

= minutes = minutes

= minutes = minutes = 6 hours 40 minutes.

So Beth takes 6 hours and 40 minutes to reach San Fransisco.

The time will be = 9:00 am + 6 hours 40 minutes = 3:40 pm.

So we have got Beth gets to San Fransisco first.

He will wait for = 20 minutes.

We have got the required answer here.

y=mx+b

step-by-step explanation:

m is slope, b is y-intercept

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3