SOLUTION: This is inequalities, Question: The maximum speed limit for a school bus is 55 mph. Write and solve an inequality that represents the number of hours it takes to travel 165 mile

Question 1033233: This is inequalities,
Question: The maximum speed limit for a school bus is 55 mph. Write and solve an inequality that represents the number of hours it takes to travel 165 miles in a school bus.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance.

when rate = 55 and distance = 165, the formula becomes 55 * time = 165.
solve for time to get time = 165 / 55 = 3 hours.

at anything less than 55, like 50, the formula becomes 50 * time = 165.
solve for time to get time = 165 / 50 = 3.3 hours.

what this says is, that if you reduce the speed below 55 miles per hours, the time it takes will be longer.

how to write this in an equality?

start with rate * time = distance
solve for rate to get rate = distance / time.
you are given that rate <= 55.
this means that distance / time <= 55, because rate = distance / time.
multiply both sides of this equation by time and divide both sides of this equation by 55 to get distance / 55 <= time.
this is the same as time >= distance / 55.
since distance = 165, you get time >= 165 / 55.
simplify this to get time >= 3 hours.

how do you get time >= distance / 55 from distance / 55 <= time.
here's how.
start with distance / 55 <= time.
subtract time from both sides of the equation to get distance / 55 - time <= 0
subtract distance / 55 from both sides of the equation to get -time <= -distance / 55.
multiply both sides of this equation by -1 to get time >= distance / 55.
the inequality is reversed, because .....
when you multiply or divide both sides of an inequality by a negative number, the inequality is reversed.

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