A boat travels 5 km upstream and 5 back. The time for the round trip is 4 hrs. The speed of the stream is 3km/hr. What is the speed of the boat in still water

Answer 1

5 = (r+3)*(4-t )= 4r - rt + 12 - 3t

5 = (r-3)*t = rt - 3t

4r - rt + 12 - 3t = rt - 3t

4r - rt + 12 = rt

4r + 12 = 2rt

2r + 6 = rt

2(r+3)/r = t

5 = (r-3)*t = 2(r-3)(r+3)/r

5r = 2 (r +3)(r-3)

0 = 2(r+3)(r-3) - 5r

0 = 2(r^2 - 9) - 5r

0 = 2r^2 - 18 - 5r

0 = 2r^2 - 5r - 18

0 = ( 2r - 9)(r + 2 )

2r-9 = 0 ---> r = 9/2 = 4.5 while r+2=0 results in negative measures

5 = (9/2 -3)* t

5 = (9/2 - 6/2)*t

5 = 3/2 * t

t = 10/3 = 3 and 1/3 hr = 3 hours and 20 minutes

3 hours and 20 minutes at 1.5 km/hr = 10/3 * 3/2 = 30/6 = 5

40 minutes at 7.5 km/hr = 2/3 * 15/2 = 30/6 = 5

The speed of the boat is 4.5 km/hr