Irodov 01

A motorboat going downstream overcame a raft at a point A. 60 min later it turned back and after some time passed the raft at a distance 6.0 km from the point A. Find the river velocity assuming the duty of the engine to be constant.

\(B_1B_2\) = \( (v_b \, + v_r\, )t_1 \)

\(R_1R_2\) = \( v_r \, t_1 \)

\(B_2B_3\) = \( (v_b \, - v_r\, )t_2 \)

\(R_2R_3\) = \( v_r \, t_2 \)

\( B_1B_2 - B_2B_3 = R_1R_2 + R_2R_3 \)

\( (v_b \, + v_r\, )t_1 \) \( - \, (v_b \, - v_r\, )t_2 \) \(= v_r \, t_1 \) \( + \, v_r \, t_2 \)

\( v_b \, t_1 + \cancel {v_r \, t_1 } - v_b \,t_2 + \cancel {v_r \, t_2 } = \cancel {v_r \, t_1 } + \cancel {v_r \, t_2} \)

\( t_2 = t_1 \) \( = 1 \; \; hour \)

\(R_1R_3\ = \) \( v_r \, t_1 + v_r \, t_2 = 6 \; km \)

\( v_r = 3 \; kmph \)