Question

1. ice on a lake gets thicker as long as the temperature is below freezing. on a certain lake it took 8 days for the ice to reach a thickness of 3 inches.

(a) at what rate was the ice growing over these 8 days in inches per day? do not round your decimal answer.
(b) ice is safe to walk on when it is 10 inches thick. would this ice be safe after 3 weeks if it grew at the rate in (a)?
(c) the ice will stop growing if it reaches a thickness of 1.5 feet. at the rate in (a), how many days of freezing would this take? first, think about how many inches 1.5 feet represents.

Explanation:

Step1: Calculate ice - growth rate

The ice reaches a thickness of 3 inches in 8 days. The rate $r$ is given by the formula $r=\frac{\text{thickness}}{\text{time}}$. So $r = \frac{3}{8}=0.375$ inches per day.

Step2: Calculate thickness after 3 weeks

3 weeks have $3\times7 = 21$ days. Using the rate $r = 0.375$ inches per day, the thickness $d$ after 21 days is $d=r\times t=0.375\times21 = 7.875$ inches. Since $7.875<10$, the ice is not safe.

Step3: Convert 1.5 feet to inches

Since 1 foot = 12 inches, 1.5 feet is $1.5\times12 = 18$ inches.

Step4: Calculate time to reach 1.5 - feet thickness

Using the rate $r = 0.375$ inches per day and the formula $t=\frac{d}{r}$, we have $t=\frac{18}{0.375}=48$ days.

Answer:

(a) 0.375 inches per day
(b) No
(c) 48 days