A motorboat that travels with a speed of 20km/hr is in still water has traveled 36 km against the current and 22km with the current, having spent 3 hours on the entire trip. Find the speed of the current of the lake.

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anonymous · Answer

@jim_thompson5910  @ganeshie8  @Mertsj  Help

jim_thompson5910 · Answer

Let

b = speed of boat in still water

c = speed of current

jim_thompson5910 · Answer

since "A motorboat that travels with a speed of 20km/hr is in still water", we know that b = 20

jim_thompson5910 · Answer

now set up the distance/rate/time equations for upstream and downstream and solve for t in each case


upstream:

d = rt

36 = (b - c)*t

36 = (20 - c)*t

t = 36/(20-c)


downstream:


d = rt

22 = (b + c)*t

22 = (20 + c)*t

t = 22/(20+c)

jim_thompson5910 · Answer

now the two times must add to 3 hours, so this means

time1 + time2 = 3

36/(20-c) + 22/(20+c) = 3

solve for c