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?

Question

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?

Bytelearn · Accepted Answer

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. Speed in feet per hour: 150 feet/hour. 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. Speed in feet per minute = 150 feet/hour ÷ 60 minutes/hour = 2.5 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. Since speed is equal to distance divided by time, we can express the time, m, it takes to travel 250 feet as m = distance/speed.Substitute Known Values: We substitute the known values into the inequality. m = 250 feet / 2.5 feet/minute.Solve for Time: Now, we solve for m. m = 250 feet / 2.5 feet/minute = 100 minutes. 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. 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 ≤ 100.

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