Journey

The road from A to B measures 11.5 km. Firstly up the hill, then by level plane and then downhill. Tourist goes uphill at 3 km/h, on the plane at 4 km/h, and downhill at 5 km/h. From the point, A to B went 2 hours 54 min back 3 hours 6 min. How long is the segment of the level plane?

Correct answer:

y =  4 km

Step-by-step explanation:

s=11.5 km t1=2:54=2 hr 54 min =2+6054=2.9 hr=2.9 t2=3:6=3 hr 6 min =3+606=3.1 hr=3.1  v1=3 km/h v2=4 km/h v3=5 km/h  x+y+z=s x/v1+y/v2+z/v3=t1 x/v3+y/v2+z/v1=t2 x+y+z=11.5 x/3+y/4+z/5=2.9 x/5+y/4+z/3=3.1  x+y+z=11.5 20x+15y+12z=174 12x+15y+20z=186  Pivot:Row1Row2 20x+15y+12z=174 x+y+z=11.5 12x+15y+20z=186  Row2201 Row1Row2 20x+15y+12z=174 0.25y+0.4z=2.8 12x+15y+20z=186  Row32012 Row1Row3 20x+15y+12z=174 0.25y+0.4z=2.8 6y+12.8z=81.6  Pivot:Row2Row3 20x+15y+12z=174 6y+12.8z=81.6 0.25y+0.4z=2.8  Row360.25 Row2Row3 20x+15y+12z=174 6y+12.8z=81.6 0.133z=0.6  z=0.133333330.6=4.5 y=681.612.8z=681.612.8 4.5=4=4 km x=2017415y12z=2017415 412 4.5=3  x=3 y=4 z=29=4.5



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