Question

Systems of Equations:

a boat traveled 210 miles downstream and back. the trip downstream took 10 hours. the trip back took 70 hours. what is the speed of the boat in still water? what is the speed of the current?


Need to show step by step. Thanks in advance.

Answer 1

`v_b-the\ speed\ of\ the\ boat\\v_c-the\ speed\ of\ the\ current\\\\v_b+v_c=(210)/(10)=21\ (mph)\\\\v_b-v_c=(210)/(70)=3\ (mph)\\\\ +\left\{\begin{array}{ccc}v_b+v_c=21\\v_b-v_c=3\end{array}\right\\-----------\\.\ \ \ \ \ \ 2v_b=24\ \ \ \ /:2\\.\ \ \ \ \ \ \ \ \ v_b=12\ (mph)\\\\12+v_c=21\\v_c=21-12\\v_c=9\ (mph)`


`Answer:\\the\ speed\ of\ the\ both\ is\ 12mph\\the\ speed\ of\ the\ current\ is\ 9mph`