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klio [65]
3 years ago
15

traveled Downstream a distance of 33 Mi and then came right back. If the speed of the current was 12mph and the total trip took

3 hours and 40 minutes,find the average speed of the boat relative to the water. The boat had an average of what speed in MPH?
Mathematics
1 answer:
spayn [35]3 years ago
7 0
<span>Traveled Downstream a distance of 33 Mi and then came right back. If the speed of the current was 12 mph and the total trip took 3 hours and 40 minutes.
Let S = boat speed in still water then                                                                         (s + 12) = downstream speed                                                                                  (s -12) =  upstream speed 
     Given Time = 3 hours 40 minutes = 220 minutes   = (220/60) h = (11/3) h                      Time = Distance/Speed
                  33/(s +12) + 33/(s-12) = 11/3                                                                               3{33(s-12) + 33(s +12)} = 11(s+12) (s -12)                                                          99(s -12 + s + 12) = 11(</span> s^{2} + 12 s -12 s -144)                                                   99(2 s) = 11(s^{2} -144)                                                                                        198 s/11 = (s^{2} -144)                                                                                         18 s = (s^{2} -144)                                                                                            (s^{2} - 18 s - 144) = 0                                                                                         s^{2} - 24 s + 6 s -144 =0                                                                                       s(s- 24) + 6(s -24) =0                                                                                            (s -24) (s + 6) = 0                                                                                                  s -24 = 0, s + 6 =0                                                                                                s = 24, s = -6                                                                     Answer) s = 24 mph is the average speed of the boat relative to the water.  
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