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
+23246 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
