Question

In reaching her destination, a backpacker walks with an average velocity of 1.05 m/s, due west. This average velocity results, because she hikes for 5.66 km with an average velocity of 2.54 m/s due west, turns around, and hikes with an average velocity of 0.403 m/s due east. How far east did she walk (in kilometers)?

Answer 1

An average velocity which will be given by -

_avg = s / t

We know that, _avg = (d_west - d_east) / (t_west + t_east)

where, t_west = (d_west / v_west) and t_east = (d_east / v_east)

then, we get

_avg = (d_west - d_east) / [(d_west / v_west) + (d_east / v_east)]

[(d_west / v_west) + (d_east / v_east)] = (d_west - d_east) / _avg

[(d_west / v_west) + (d_east / v_east)] = (d_west / _avg) - (d_east / _avg)

(d_east / v_east) + (d_east / _avg) = (d_west / _avg) - (d_west / v_west)

d_east [(1 / v_east) + (1 / _avg)] = d_west [(1 / _avg) - (1 / v_west)]

d_east [(_avg + v_east) / _avg v_east] = d_west [(v_west - _avg) / _avg v_west]

d_east = d_west [(v_west - _avg) / _avg v_west] [_avg v_east / (_avg + v_east)]

d_east = d_west (v_east / v_west) [(v_west - _avg) / (v_east + _avg)]

d_east = (5.66 km) [(0.403 m/s) / (2.54 m/s)] {[(2.54 m/s) - (1.05 m/s)] / [(0.403 m/s) + (1.05 m/s)]}

d_east = (5.66 km) (0.1586) (1.0254)

d_east = 0.92 km