Question

Calculator Reference 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

so he climbed the first 1000ft in 1000/x hours then

the rate of the 5000ft is "10 feet per hour less than twice the first rate", so hmm twice the first rate is 2x, 10 less than that is 2x - 10.

so, the 5000ft were climbed in 5000/(2x-10)

the number of hours it lasted climbing? well, simply add them up.

Answer 2

Answer: The expression that represents the number of hours the mountaineer climbed is given by

$\dfrac{1000}{x}+\dfrac{2500}{x-5}$

Step-by-step explanation:

Since we have given that

Distance covered by mountaineer = 1000 feet

Speed at which he climbed = x feet per hour

Time taken by him would be

$\dfrac{1000}{x}$

Additional distance covered by him = 5000 feet

Speed at which he climbed this time = 2x-10

So, Time taken is given by

$\dfrac{5000}{2x-10}\\\\\\=\dfrac{5000}{2(x-5)}\\\\\\=\dfrac{2500}{x-5}$

Hence, the expression that represents the number of hours the mountaineer climbed is given by

$\dfrac{1000}{x}+\dfrac{2500}{x-5}$