Algebra 1 help please

Question

can you help me solve this? starting from 50 miles away a car drives towards a speed check point and then passes it.The car travels at a constant rate of 30 miles per hour. The distance of the car from the checkpoint is given by d=l50-30t|. At what times is the car 5 miles away from the check point?

Answer 1

asking when you're 5 miles away is the same as asking when have you gone 45 miles

you start 50 miles away. When you've gone 45 miles, you are 5 miles away from the check point

d=rt, distance = rate of speed x time or

t=d/r = 45/30 = 90/60 = 1 1/2 hours = 90 minutes

or use the distance equation, and ignore the absolute value signs to get

d= 5 = 50-30t

30t = 45

t = 45/30 = 1 1/2 hours

there's a 2nd solution though, where you interpret the absolute value signs to also mean

5= -(50-30t)

5=-50 + 30t

t= 55/30 = 11/6 hours = 1 5/6 hours = 110 minutes = 1 hour and 50 minutes

this is also correct if you include overrunning the check point and go 5 miles past it.

Answer 2

In order to solve this, you must get rid of the absolute value sign. The resulting equations will be as follows:

d=50-30t

-d=50-30t

Then you plus in 5 for d in both these equations and solve for t. I hope this helps!