The start of a hike, a hiker was at an elevation of –50 feet (where 0 represents sea level). The hiker climbs at a rate of 15 feet per minute.
a) Write an inequality that represents t, the number of minutes after the start of the hike, when the hiker’s elevation was higher than 5 feet above sea level. Explain or show your thinking.
To write an inequality representing t, the number of minutes after the start of the hike when the hiker's elevation was higher than 5 feet above sea level, we can use the following equation:
-50 + 15t > 5
In this equation, -50 represents the initial elevation of the hiker, 15 represents the rate at which the hiker is climbing (15 feet per minute), t represents the number of minutes after the start of the hike, and 5 represents 5 feet above sea level.
By adding 5 to both sides of the equation, we get:
-50 + 15t + 5 > 5 + 5
which simplifies to:
-45 + 15t > 10
Next, we add 45 to both sides of the equation to isolate 15t:
-45 + 45 + 15t > 10 + 45
which simplifies to:
15t > 55
Finally, we divide both sides of the equation by 15 to solve for t:
(15t)/15 > 55/15
which simplifies to:
t > 11/3
Therefore, the inequality that represents t, the number of minutes after the start of the hike when the hiker's elevation was higher than 5 feet above sea level, is t > 11/3.