Question

A mountaineer climbed 1000 feet at a rate of x feet per hour .he climbed an additional 5000 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

(1000(2x - 10) + 5000x) / (x(2x - 10))

Explanation:

Let's represent the mountaineer's first rate of climbing (in feet per hour) as "x." According to the given information, the second rate of climbing is 10 feet per hour less than twice the first rate, so it can be expressed as "2x - 10" feet per hour.

The mountaineer climbed 1000 feet at the first rate and an additional 5000 feet at the second rate. We can now set up the equation to find the number of hours he climbed.

Distance climbed at the first rate + Distance climbed at the second rate = Total distance climbed

(1000 feet) + (5000 feet) = Total distance climbed

To find the time (in hours) taken to climb each distance, we divide the distance climbed by the respective rate:

Time taken to climb at the first rate: 1000 feet / x feet per hour = 1000/x hours

Time taken to climb at the second rate: 5000 feet / (2x - 10) feet per hour = 5000 / (2x - 10) hours

Now, we can set up the equation:

1000/x hours + 5000/(2x - 10) hours = Total number of hours climbed

To find the total number of hours the mountaineer climbed, we need to combine the fractions:

Total number of hours climbed = (1000(2x - 10) + 5000x) / (x(2x - 10))

Thus, the expression representing the number of hours the mountaineer climbed is:

(1000(2x - 10) + 5000x) / (x(2x - 10))