Question

Manuel is hiking up a mountain. After 3 hours, he is 2500 feet from the summit. After 5 hours, he is 1300 feet from the summit. What is the height, in feet, of the mountain?

Answer 1

Answer:

 Height of summit = 4300 ft

Explanation:

 Let the height of summit be h.

 After 3 hours, he is 2500 feet from the summit,

 Height traveled = (h - 2500)

 Time taken = 3 hours

  Speed = (h-2500)/3

 After 5 hours, he is 1300 feet from the summit

  Height traveled = (h - 1300)

  Time taken = 5 hours

  Speed = (h-1300)/5

Here speed is same, so we have

    $\frac{h-2500}{3} =\frac{h-1300}{5}\\ \\ h-2500=0.6(h-1300)\\ \\ h-0.6h=2500-0.6*1300\\ \\ h=4300ft$

  Height of summit = 4300 ft