Question

A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours he climbed

Answer 1

Using distance=rate multiplied by time as the formula,

mountaineer climbed 1,000 feet at a rate of x feet per hour
1000 = xt1 <--eq.1

"He climbed an additional 5,000 feet at a different rate."
5000 = x't2 <--eq.2

"This rate was 10 feet per hour less than twice the first rate."
x' = 2x - 10 <--eq.3

We now have 3 equations/expressions to solve for the number of hours:
From eq. 1 and 2:
Total time = t1 +t2 = t
t = 1000/x + 5000/x'
but x' = 2x - 10
t = 1000/x + 5000/(2x-10)
t = 1000/x + 5000/[2(x-5)]
t = 1000/x + 2500/(x-5) <--ANSWER