Question

a mountaineer 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?

Answer 1

`(1000)/(x) +(2500)/(x-5)`

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 =
`(1000)/(x)`

Additional distance covered by him = 5000 feet

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

So, total time T =
`(1000)/(x) +(5000)/(2(x-5))`

T =
`(1000)/(x) +(2500)/(x-5)`

Answer 2

A mountaineer climbed 1000 feet at a rate of x feet/hour

1000 = x ( t 1 ) eq1

5000 = X ( t 2) eq2 ( he climbed additional at different rate )

the rate was 10 feet / hour less than twice the first rate

X = 2x - 10 eq3

take eq1 and eq 2

( total time = t 1 + t 2 = 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)