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

Height of summit = 4300 ft

Step-by-step 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

`(h-2500)/(3) =(h-1300)/(5)\\ \\ h-2500=0.6(h-1300)\\ \\ h-0.6h=2500-0.6*1300\\ \\ h=4300ft`

Height of summit = 4300 ft