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.
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.
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