Question

In reaching her destination, a backpacker walks with an average velocity of 1.26 m/s, due west. This average velocity results, because she hikes for 6.15 km with an average velocity of 2.46 m/s due west, turns around, and hikes with an average velocity of 0.630 m/s due east. How far east did she walk (in kilometers)? (Please show work)

dw VE West East de

Answer 1

Let t be the total time she walked, t1 the time she walked west and t2 the time she walked east

So the answer to the problem x(east) = 0.630m/s*t2

Now to find t2

we have t = t1 + t2 but t1 = 6150m/2.46m/s = 2500s

so t = 1841 + t2

Now the distance covered = 1.26m/s*t = 6150m - 0.630m/s*t2

rewriting 1.26*(2500 + t2) = 6150 - 0.630*t2

or 1.89*t2 = 6150 - 1.26*2500

so t2 = 8648.74/1.89 = 4576.052s

So the distance she waked east is 0.630m/s*4576.052s = 2882.912m = 2.882912 km