Tatra

A tourist climbed from a hut at an altitude of 1367 m above sea level to the top of the Tatra Peak. The trip there and back took him 6 hours and 20 minutes. What is the altitude of the mountain peak if the tourist climbed 300 meters in one hour and 500 meters in one hour? He rested for one hour during the hike.

Correct answer:

h =  2367 m

Step-by-step explanation:


a+b+1 = 6+20/60
300 a = h-1367
500 b = h-1367

a+b+1 = 6+20/60
300·a = h-1367
500·b = h-1367

60a+60b = 320
300a-h = -1367
500b-h = -1367

Pivot: Row 1 ↔ Row 2
300a-h = -1367
60a+60b = 320
500b-h = -1367

Row 2 - 60/300 · Row 1 → Row 2
300a-h = -1367
60b+0.2h = 593.4
500b-h = -1367

Pivot: Row 2 ↔ Row 3
300a-h = -1367
500b-h = -1367
60b+0.2h = 593.4

Row 3 - 60/500 · Row 2 → Row 3
300a-h = -1367
500b-h = -1367
0.32h = 757.44


h = 757.44/0.32 = 2367
b = -1367+h/500 = -1367+2367/500 = 2
a = -1367+h/300 = -1367+2367/300 = 3.33333333

a = 10/3 ≈ 3.333333
b = 2
h = 2367

Our linear equations calculator calculates it.



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