A bus heading to Belfast leaves Antrim every 36 minutes. A bus heading to Ballymena leaves Antrim every 45 minutes.
At 10am the bus to Belfast and the bus to Ballymena both leave Antrim Bus station.
Work out the next time the buses both leave at the same time?

Step-by-step explanation:

We are given the position function and need to find the value of t when h<17.

Create an inequality that represents this situation:

The "less than" sign makes this very specifically a conjunction problem as opposed to a disjunction. That's important to the solution. But we'll get there.

The simplest way to solve this is to subtract 81 from both sides:

then divide both sides by -16:

Notice now that the sign is facing the other way since we had to divide by a negative number. Now it's a disjunction. The solution set to this inequality is that t>2 or t<-2. First and foremost, time will never be negative, so we can disregard the -2. Even if that was t<2, the more time that goes by, the greater the time interval is, not the lesser. It's the "<" that doesn't make sense, not only the -2. The solution to this inequality is

t > 2 sec. That means that after 2 seconds, the height of the ball is less than 17 feet.