A water skiing instructor recommends that a boat pulling a beginning skier have a speed less than 18 miles per hour. Write and solve an inequality that you can use to find the possible distances d (in miles) that a beginner can travel in 45 minutes of practice time
A water skiing instructor recommends that a boat pulling a beginning skier have a speed less than 18 miles per hour. Write and solve an inequality that you can use to find the possible distances d (in miles) that a beginner can travel in 45 minutes of practice time
Well, looks like we need to find an inequality to limit the distance a beginner skier can travel in 45 minutes. Let's break it down!
We know that the speed needs to be less than 18 miles per hour. But we need to convert that into miles per minute since we want to find the distance for 45 minutes.
So, if the speed in miles per hour is less than 18, we can set up the inequality like this:
Speed < 18 miles/hour
Since there are 60 minutes in an hour, we divide the speed by 60 to get the speed in miles per minute:
Speed < 18/60 miles/minute
Simplifying further, we have:
Speed < 0.3 miles/minute
Now, let's substitute the formula for speed, which is distance divided by time:
Distance/Time < 0.3 miles/minute
Since the practice time is 45 minutes, we have:
Distance/45 < 0.3 miles/minute
To find the possible distance d (in miles) a beginner can travel in 45 minutes, we multiply both sides of the inequality by 45:
Distance < 0.3 miles/minute * 45 minutes
Distance < 13.5 miles
So, the possible distances d (in miles) that a beginner can travel in 45 minutes of practice time is less than 13.5 miles.
Keep in mind that this inequality assumes a constant speed throughout the entire 45 minutes of practice. Happy skiing!
To solve this problem, let's first convert the time of practice from minutes to hours.
45 minutes is equivalent to 45/60 = 0.75 hours.
Now, let's set up the inequality using the given information.
Since the instructor recommends a speed less than 18 miles per hour, we can write:
Speed < 18 mph
We know that speed is the ratio of distance to time. So, distance can be calculated by multiplying speed by time, which gives us:
Distance = Speed × Time
Substituting the values we have, we get:
Distance = Speed × 0.75
Now, we can substitute this expression into the inequality:
Speed × 0.75 < 18
To solve for distance, divide both sides of the inequality by 0.75:
Distance < 18 / 0.75
Simplifying, we have:
Distance < 24
Therefore, the possible distances a beginner can travel in 45 minutes of practice time are less than 24 miles.
To solve this problem, we need to use the formula Distance = Rate × Time, where the rate is the speed of the boat and the time is given as 45 minutes (which we will convert to hours).
Let's start by converting 45 minutes to hours. Since there are 60 minutes in an hour, we divide 45 minutes by 60:
45 minutes ÷ 60 = 0.75 hours
Now, let's use the formula Distance = Rate × Time and replace Time with 0.75 hours.
Distance = Rate × 0.75
Since the rate should be less than 18 miles per hour according to the instructor's recommendation, we can write the inequality as:
Rate < 18
Substituting Rate with d (distance) in the inequality, we get:
d < 18 × 0.75
Simplifying:
d < 13.5
Therefore, the inequality that represents the possible distances a beginner can travel in 45 minutes is:
d < 13.5 miles