Question

Jenny and julian are hiking jenny starts at an elevation of 480 feet and is hiking down a mountain at a constant rate of 15 feet per minute so her elevation is decreasing 15 feet every minute at the same time julian starts at an elevation of 200 feet and is hiking at a rate of 5 feet per minute so her elevation is increasing at a rate of 5 feet every minute. the variable T represents the time in minutes they have been hiking. When will the two hikers be at the same elevation?

Answer 1

Time taken for both hikers to be at the same elevation = 14 minutes

At that time, they will both be at an elevation of 270 feet

Explanation:

Let us represent Jenny's current elevation by x and Julian's current elevation by y

Let T be the time taken when the hikers reach the same elevation

For Jenny

• Initially Jenny's elevation is at 480 feet

• Her rate of descent (vertically) is 15 feet per minute
• So in T minutes she would have descended 15T feet.

• Jenny's elevation after T minutes = 480 - 15T feet

For Julian

• Initial elevation = 200 feet

• Rate of vertical ascent = 5 feet /minute

• After T minutes, vertical ascent = 5T minutes

• His elevation would be : 200 + 5T

• Since at this point in time, the elevation of both hikers is equal,
  200 + 5T = 480 - 15T

• Add 15T to both sides:
  200 + 5T + 15T = 480 - 15T + 15T
  ==> 200 + 20T = 480

• Subtract 200 from both sides:
  200 - 200 + 20T = 480 - 200
  20T = 280
  T = 280/20 = 14 minutes

Check working
After 14 minutes, Jenny's elevation = 480 - 15 x 14 = 480 = 210 = 270 feet

After 14 minutes, Julian's elevation = 200 + 5 x 14 = 200 + 70 = 270 feet

So it checks out