Determine 7314

The hiker went from A to B and back in 3 hours and 41 minutes. The road from A to B is first uphill, then flat, and finally downhill. A hiker walked up a hill at a speed of 4 km/h, on a flat surface at a speed of 5 km/h, and down a hill at a speed of 6 km/h. The distance between A and B is 9 km. Determine the length of the path along the plane.

Correct answer:

y =  4 km

Step-by-step explanation:


x+y+z=9
x/4+y/5+z/6 = (3+41/60) / 2
x/6+y/5+z/4 = (3+41/60) / 2

x+y+z = 9
15x+12y+10z = 110.5
10x+12y+15z = 110.5

Pivot: Row 1 ↔ Row 2
15x+12y+10z = 110.5
x+y+z = 9
10x+12y+15z = 110.5

Row 2 - 1/15 · Row 1 → Row 2
15x+12y+10z = 110.5
0.2y+0.333z = 1.633
10x+12y+15z = 110.5

Row 3 - 10/15 · Row 1 → Row 3
15x+12y+10z = 110.5
0.2y+0.333z = 1.633
4y+8.333z = 36.833

Pivot: Row 2 ↔ Row 3
15x+12y+10z = 110.5
4y+8.333z = 36.833
0.2y+0.333z = 1.633

Row 3 - 0.2/4 · Row 2 → Row 3
15x+12y+10z = 110.5
4y+8.333z = 36.833
-0.083z = -0.208


z = -0.20833333/-0.08333333 = 2.5
y = 36.83333333-8.3333333333333z/4 = 36.83333333-8.33333333 · 2.5/4 = 4
x = 110.5-12y-10z/15 = 110.5-12 · 4-10 · 2.5/15 = 2.5

x = 5/2 = 2.5
y = 4
z = 5/2 = 2.5

Our linear equations calculator calculates it.



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