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# pls help

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a boat travels downstream for a distance of 36km, then travel upstream back to its starting point. The boat takes 1 hour more to travel upstream. If the speed of boat in still water is 15km/h, find the speed of the water current

Apr 18, 2020

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Formula:  Distance  =  Rate x Time     --->     D  =  RT

Speed of boat in still water:  15 km/hr

Speed of the water current:  w

Distance downstream =  36 km                   Distance upstream =  36 km

Rate downstream       =  15 + w                  Rate upstream        =  15 - w

Time downstream       =  t                           Time upstream       =  t + 1

Formula downstream:  36  =  (15 + w)(t)    Formula upstream:  36  =  (15 - w)(t + 1)

36/(15 + w)  =  t                                        36/(15 - w)  =  t + 1

36/(15 - w) - 1  =  t

Putting these two equations together:  36/(15 + w)  =  36/(15 - w) - 1

Multiplying by (15 + w)(15 - w):              36(15 - w)  =  36(15 + w) - (15 + w)(15 - w)

540 - 36w  =  540 + 36w - (225 - w2)

-72w  =  -225 + w2

w2 + 72w - 225  =  0

(w + 75)(w - 3)  =  0

Either  w  =  -75 (discard)  or  w  =  3 km/hr

Apr 18, 2020