Question

davis digs a hole at a rate of $\frac{3}{4}$ feet every 10 minutes. after digging for 40 minutes, davis places a bush in the hole that fills exactly $\frac{7}{8}$ feet of the hole. relative to ground level, what is the elevation of the hole after placing the bush in the hole? enter your answer as a simplified mixed number in the box

Explanation:

Step1: Calculate the depth of the hole before placing the bush

Since the rate of digging is $\frac{3}{4}$ feet every 10 minutes, and the time of digging is 40 minutes. The number of 10 - minute intervals in 40 minutes is $\frac{40}{10}=4$. So the depth of the hole before placing the bush is $\frac{3}{4}\times4 = 3$ feet.

Step2: Calculate the depth of the hole after placing the bush

We subtract the height of the bush from the depth of the hole before placing the bush. Let $d$ be the depth of the hole after placing the bush. Then $d=3-\frac{7}{8}$. We rewrite 3 as $\frac{24}{8}$ (since $3=\frac{3\times8}{8}$), so $d=\frac{24}{8}-\frac{7}{8}=\frac{24 - 7}{8}=\frac{17}{8}$.

Step3: Convert the improper - fraction to a mixed number

We divide 17 by 8. $17\div8 = 2$ with a remainder of 1. So $\frac{17}{8}=2\frac{1}{8}$ feet.

Answer:

$2\frac{1}{8}$ feet