Question

A butterfly is flying 8 3/4 feet above the ground. It descends at a steady rate to a spot 6 1/4 feet above the ground in 1 2/3 minutes. What is the butterfly’s change in elevation each minute?

Answer 1

The butterfly changes elevation at a rate of 1 1/2 feet per minute. This is calculated by determining the total change in elevation, which is 2 1/2 feet, and dividing it by the total time, which is 1 2/3 minutes, after converting them to improper fractions.

Step-by-step explanation:

To calculate the butterfly's change in elevation each minute, we need to first find the total change in elevation and then divide by the total time in minutes. The butterfly descends from 8 3/4 feet to 6 1/4 feet. The change in elevation is the difference between these two measurements.

First, convert the mixed numbers to improper fractions:

6 1/4 feet = (6 × 4 + 1)/4 = 25/4 feet

Now, subtract the final elevation from the starting elevation to find the change:

(35/4) - (25/4) = (35 - 25) / 4 = 10/4 feet

10/4 feet simplifies to 2 1/2 feet, which is the total change in elevation.

Since the butterfly descends this distance in 1 2/3 minutes, we'll convert 1 2/3 minutes to an improper fraction, which is (1 × 3 + 2)/3 = 5/3 minutes.

To find the change in elevation per minute, divide the change in elevation by the time:

(2 1/2) / (5/3)

Converting 2 1/2 to an improper fraction gives us 5/2, so our calculation is:

(5/2) ÷ (5/3) = (5/2) × (3/5) = 15/10 = 1 1/2 feet per minute

Therefore, the butterfly's change in elevation is 1 1/2 feet per minute.

Answer 2

Step-by-step explanation:

6¼ ft - 8¾ ft = -2½ ft

(-2½ ft)/(1⅔ min) = (5/2 ft)/(5/3 min)

= (5/2)/(5/3) ft/min

= (5/2 × 3/5 ft)/min

= 1.5 ft /min