In reaching her destination, a backpacker walks with an average velocity of 1.28

Question

In reaching her destination, a backpacker walks with an average velocity of 1.28 m/s, due west. This average velocity results, because she hikes for 5.92 km with an average velocity of 2.38 m/s due west, turns around, and hikes with an average velocity of 0.632 m/s due east. How far east did she walk (in kilometers)?

Explanation / Answer

Let she walk x km due East. Then total distance = (5.92+x)*1000 Time taken during West direction walk = 5920/2.38 = 2487.394958 seconds Time taken during East direction walk = x*1000/0.632 = 1582.278481x seconds Total time = 2487.394958 + 1582.278481x =>Average velocity = Total distance/Total Time = ((5.92+x)*1000)/(2487.394958 + 1582.278481x) =>1.28 = (5.92+x)/(2.487394958+1.582278481x) =>3.183865546+2.025316456x = 5.92+x =>1.025316456x = 5.92-3.183865546 =>x = 2.6686 KM

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