Water and other materials necessary for biological activity in trees are absorbed by the roots and transported throughout the stem and branches in thin, hollow tubes in the xylem. Water may travel as fast as $150$ feet per hour. Which of the following inequalities best describes the number of minutes, $m$ , after being absorbed by the root, that it takes for water to reach a height of $250$ feet above the ground?

View step-by-step help

Home

Math Problems

Grade 8

Solve equations with variables on both sides: word problems

Full solution

Q. Water and other materials necessary for biological activity in trees are absorbed by the roots and transported throughout the stem and branches in thin, hollow tubes in the xylem. Water may travel as fast as

150

feet per hour. Which of the following inequalities best describes the number of minutes,

m

, after being absorbed by the root, that it takes for water to reach a height of

250

feet above the ground?

Convert Speed to Minutes: First, we need to convert the speed of water travel from feet per hour to feet per minute to make it compatible with the time in minutes. $\newline$ Speed in feet per hour: $150$ feet/hour. $\newline$ There are $60$ minutes in an hour, so we divide the speed by $60$ to get the speed in feet per minute.
Calculate Speed in Feet: Now, we calculate the speed in feet per minute. $\newline$ Speed in feet per minute = $150 \, \text{feet/hour} \div 60 \, \text{minutes/hour} = 2.5 \, \text{feet/minute}.$
Set Up Inequality: Next, we need to set up an inequality that represents the time it takes for water to travel $250$ feet. $\newline$ Since speed is equal to distance divided by time, we can express the time, $m$ , it takes to travel $250$ feet as $m = \frac{\text{distance}}{\text{speed}}$ .
Substitute Known Values: We substitute the known values into the inequality. $m = \frac{250 \text{ feet}}{2.5 \text{ feet/minute}}$ .
Solve for Time: Now, we solve for $m$ . $\newline$ $m = \frac{250 \text{ feet}}{2.5 \text{ feet/minute}} = 100 \text{ minutes}.$ $\newline$ This means that it takes $100$ minutes for the water to reach a height of $250$ feet.
Write Final Inequality: Finally, we write the inequality that describes the number of minutes, $m$ , after being absorbed by the root, that it takes for water to reach a height of $250$ feet above the ground. $\newline$ Since the water can travel as fast as $150$ feet per hour, it could take less than or equal to $100$ minutes to reach $250$ feet. Therefore, the inequality is $m \leq 100$ .