Question 1164552: Danny is taking a road trip. After 36 miles, he reaches a stretch of highway with a speed limit of 60 miles/hour. Danny is trying to figure out the minimum number of hours he’ll need to drive to reach over 300 total miles for the trip, assuming he stays under or at the speed limit.
He creates the inequality 60t + 36 ≥ 300, where t is the time elapsed, in hours.
What statement is the most accurate?
A.
Danny needs at least 7 hours to drive 300 miles.
B.
Danny may drive 300 miles in 5 hours.
C.
At 4 hours, Danny will have just driven 300 miles.
D.
It isn’t possible to drive 300 miles before the day is over.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he has to drive at 60 miles per hour or less.
assuming he drives at 60 miles per hour, then
60t + 36 = 300 gets you t = 4/4 hours.
A is no good because he can easily do it in less than 7 hours.
D is no good because you don't know when he started and so there's no way of knowing whether he can make it by the end of the day of not.
C is no good because, if he travels at 60 miles per hour, it will take him 4.4 hours to reach 300 miles.
the only way he can do it in 4 hours is to travel more than 60 miles per hour.
for example:
x * 4 + 36 = 300
x is the speed
4 is the time in hours.
you get 4x = 264
solve for x to get x = 66
that's above 60 miles per hour which means he has to go over the speed limit to achieve that.
i would say B is the best fit.
he could do 300 miles in 4.4 hours.
if he traveled less than 60 miles per hour, he could make 300 miles in 5 hours.
for example:
x * 5 + 36 = 300
x is the speed
5 is the time in hours
you get 5x = 264
solve for x to get x = 264/5 = 52.8 miles per hour.
that's below and close to 60 miles per hour.
it seems the most reasonable.
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