Aboat travels 6 km upstream and 6 km back. the time for the round trip is 10 hrs. the speed of the stream is 5 km/hr. what is the speed of the boat in still water? the speed of the boat is nothing km/hr.

Boat's Rate: r = 5.63587

Step-by-step explanation:

Givens

t = 10 hoursr = rate of the boatr1 = 5 mph which is the rate of the steam.d = 6 km

Formula

d = r * ttransposed t = d/r

Formula

d/(r + 5) + d/(r - 5) = 10

Solution

6 (1 / (r + 5) + 1 / (r - 5) ) = 10                             Divide by 6( 1 / (r + 5) + 1 / (r - 5)  ) = 10/6 = 1.6667   Multiply by the LCM on both sidesLCM = ( r + 5) * (r - 5)( r - 5 + r + 5) / ( (r + 5)(r - 5)  = 1.6667      Combine the left side(2r )/( (r - 5)(r + 5) ) = 1.6667                       Multiply by the LCM on both sides.2r  = 1.6667 * (r - 5)(r + 5)                          Divide by 2r = 0.833335 * (r - 5)(r + 5)                        Combine the right sider = 0.833335 (r^2 - 25)                              Remove the bracketsr = 0.833335*r^2 - 20.833335                 Subtract r from both sides0 = 0.833335*r^2 - r -  20.833335Use the quadratic formula to solve thisa = 0.833335 b = -1 c = -20.833335The value that comes out that matter is r = 5.63587

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