Mathematics : asked on rachelrogers85

02.04.2023

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?

Step-by-step answer

12.11.2022, solved by verified expert

Ranjana Bhatt

p PhD

Chemistry, Q&A Expert

17 481

29 136 answers

5 rating

Unlock the full answer

The answer is in the image

A mountaineer climbed 1,000 feet at a rate of, №12926670, 02.04.2023 12:00

It is was helpful?

Helpful Useless

Faq

Mathematics

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?

Step-by-step answer

P Answered by PhD

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.

Mathematics

Amountaineer climbed 1,000 feet at a rate of x feet per hour, he climbed and 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?

Step-by-step answer

P Answered by Specialist

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

Step-by-step explanation:

Total time T = (distance 1)/ (speed 1) + (distance 2)/ ( speed 2)

Distance covered by the mountaineer = 1000 feet

Speed of climbing = x feet per hour

Time taken will be = $\frac{1000}{x}$

Additional distance covered by him = 5000 feet

Speed to cover this distance = 2x-10 or 2(x-5)

So, total time T = $\frac{1000}{x} +\frac{5000}{2(x-5)}$

T = $\frac{1000}{x} +\frac{2500}{x-5}$

Mathematics

Amountaineer 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

Step-by-step answer

P Answered by PhD

Your question asks for an expression, so you would expect an answer in the form of an equation containing variables. This is because you have only 2 independent equations with 3 unknowns. That makes the system unsolvable.

Suppose v₁ is the mountaineer's velocity during the 1,000-foot trail. Then, v₂ is his speed for the 5,000-foot trail. The equation relating these two variables is:

v₂ = 2v₁ - 10 ---> equation 1

Then, you find the equation for the total number of hours he climbed. That would be the distance divided by their respective speed.

t = 1000/v₁ + 5000/v₂ > equation 2

Substituting equation 1 to equation 2,

t = 1000/v₁ + 5000/(2v₁ - 10)
t = 1000/v₁ + 5000/2(v₁-5)
t = 1,000/v₁ + 2,500/(v₁-5)

Mathematics

Step-by-step answer

P Answered by Master

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

Step-by-step explanation:

Total time T = (distance 1)/ (speed 1) + (distance 2)/ ( speed 2)

Distance covered by the mountaineer = 1000 feet

Speed of climbing = x feet per hour

Time taken will be = $\frac{1000}{x}$

Additional distance covered by him = 5000 feet

Speed to cover this distance = 2x-10 or 2(x-5)

So, total time T = $\frac{1000}{x} +\frac{5000}{2(x-5)}$