Motorboat : current

The ratio of the speed of a motorboat to that of the current is 36:5. The motorboat travels downstream in 5 hours and 10 minutes. Find the time for the motorboat to return upstream.

Result

t₂ = 6:50 hh:mm

Step-by-step explanation:

$$\begin{gathered} v:v_0=36:5=36x:5x \\ {t}_1=5:10=5hr10min=5+\frac{10}{60}=5.1667hr\doteq 5.1667 \\ {s}_1=s_2 \\ (v+v_0)\cdot t_1=(v-v_0)\cdot t_2 \\ (36x+5x)\cdot t_1=(36x-5x)\cdot t_2 \\ 41x\cdot t_1=31x\cdot t_2 \\ 41t_1=31t_2 \\ {t}_2=\frac{41}{31}\cdot t_1=\frac{41}{31}\cdot 5.1667=6.83333=6:50\text{hh}:\text{mm} \end{gathered}$$

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