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 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 =

Additional distance covered by him = 5000 feet

Speed to cover this distance = or

So, total time T =  

T =

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4