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

Answer:

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

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

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)