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 the mountaineer climbed?

Answer 1

Answer:

Step-by-step explanation:

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