anonymous
  • anonymous
A motorboat takes 4 hours to travel 128km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water? What is the rate of the current?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I was able to figure that one out. Now I've moved on to the following: two cyclists leave town 168 miles apart at the same time and travel toward each other. One cyclist travels 4 mi/h slower than the other. If they meet in 4 hours what is the rate of each cyclist?
Michele_Laino
  • Michele_Laino
If I call with v the speed of the motorboat with respect to the earth and with V the speed of the current, then the time nedded to go upstream is: \[\Large {t_a} = \frac{L}{{v - V}}\] whereas the time needed to got to downstream is: \[\Large {t_d} = \frac{L}{{v + V}}\]
Michele_Laino
  • Michele_Laino
where L= 128 Km

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Michele_Laino
  • Michele_Laino
and ta= 4 hours, td= 2 hours
anonymous
  • anonymous
Okay - I understand that...
Michele_Laino
  • Michele_Laino
so we can write this algebraic system: \[\Large \left\{ \begin{gathered} v - V = 32 \hfill \\ \hfill \\ v + V = 64 \hfill \\ \end{gathered} \right.\]
anonymous
  • anonymous
Okay
Michele_Laino
  • Michele_Laino
if we subtract the first equation from the second one, we get: \[\Large 2V = 32\] what is V?
Michele_Laino
  • Michele_Laino
@Juliette2120
Michele_Laino
  • Michele_Laino
here I call with v_A the speed of the first cyclist and with v_B the speed of the second cyclist, so I can write this: \[\Large {v_B} = {v_A} - 4\]
Michele_Laino
  • Michele_Laino
here is the situation described in your problem: |dw:1435553779177:dw|
Michele_Laino
  • Michele_Laino
we can write: \[\Large {v_A}t + {v_B}t = L\] where L=168 miles, and t=4 hours
Michele_Laino
  • Michele_Laino
after a substitution, we get: \[\large \begin{gathered} {v_A}t + \left( {{v_A} - 4} \right)t = L \hfill \\ \hfill \\ 2{v_A}t = L + 4t \hfill \\ \hfill \\ {v_A} = \frac{{L + 4t}}{{2t}} = \frac{{168 + 4 \times 4}}{{2 \times 4}} = \frac{{184}}{8} = 23\;miles/hour \hfill \\ \hfill \\ {v_B} = {v_A} - 4 = 23 - 4 = 17\;miles/hour \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
oops.. \[\Large {v_B} = {v_A} - 4 = 23 - 4 = 19\;miles/hour\]
Michele_Laino
  • Michele_Laino
sorry, for my error!
Michele_Laino
  • Michele_Laino
reassuming, the requested rates or speed, are: \[\Large \begin{gathered} {v_A} = 23\;miles/hour \hfill \\ {v_B} = {v_A} - 4 = 23 - 4 = 19\;miles/hour \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
speeds*
Abhisar
  • Abhisar
Hello @Juliette2120 ! Are you satisfied with the response? please don't forget to rate the user. Thanks.

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