Question

At the start of a hike, a hiker was at a elevation of -50 feet (where 0 represents sea level). The hiker climbs at a rate of 15 per minute. 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.

Answer 1

The inequality that represents 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 > 3.67.

Step-by-step explanation:

To represent 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 inequality:

-50 + 15t > 5

Where t represents the number of minutes after the start of the hike. To isolate t, we need to subtract -50 from both sides of the inequality:
-50 + 15t - (-50) > 5 - (-50)
15t > 55

Finally, we divide both sides of the inequality by 15 to solve for t:
t > 3.67

Therefore, the inequality that represents 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 > 3.67.

Answer 2

t > 3.66667 minutes

Step-by-step explanation:

The height of the hiker at any time is given by

H(t) = -50 + 15t

At H = 5 ft,

5 = -50 + 15t

15t = 55

t = (11/3) = 3.6667 minutes; the hiker's elevation is exactly 5 ft at this point.

From then on,

H(t) > 5 ft

-50 + 15t > 5

t > 3.6667 minutes