Question

There was a big snowstorm overnight that dumped over 12 inches of snow on Math Town. Luckily, it got a lot warmer, and 0.5 inch is melting each hour. The snow is now less than 5 inches deep. Write an inequality to determine how many hours have passed since the snow started melting.

Answer 1

The inequality to determine how many hours have passed since the snow started melting in Math Town is 12 - 0.5h < 5. Solving for h reveals that more than 14 hours have passed since the snow depth reduced to less than 5 inches.

Step-by-step explanation:

Let's represent the number of hours by h. Given that the initial depth of the snow was over 12 inches and it's melting at a rate of 0.5 inches per hour, the remaining snow depth after h hours would be 12 - 0.5h inches. Since we know that the snow is now less than 5 inches deep, the inequality to represent this situation is 12 - 0.5h < 5. To solve this inequality for h, we subtract 12 from both sides and then divide by -0.5, remembering to reverse the inequality sign because we're dividing by a negative number: -0.5h < 5 - 12, -0.5h < -7, h > 14. So more than 14 hours have passed since the snow started melting.