A boat sails 40 km downstream and then 40 km upstream in a river. The boat's speed in still water is 12 km/hr and the speed of the stream is 4 km/hr. How much time does the boat take to cover the entire distance (both upstream and downstream)?
7.5 hours
To determine how much time the boat takes to cover the entire distance of 40 km downstream and 40 km upstream, we need to calculate the time taken for each journey and then sum these times. Here's the step-by-step solution:
\(v_{\text{downstream}} = v_{\text{boat}} + v_{\text{stream}} = 12 \,\text{km/hr} + 4 \,\text{km/hr} = 16 \,\text{km/hr}\)
\(t_{\text{downstream}} = \frac{\text{distance}}{\text{speed}} = \frac{40 \,\text{km}}{16 \,\text{km/hr}} = 2.5 \,\text{hours}\)
\(v_{\text{upstream}} = v_{\text{boat}} - v_{\text{stream}} = 12 \,\text{km/hr} - 4 \,\text{km/hr} = 8 \,\text{km/hr}\)
\(t_{\text{upstream}} = \frac{\text{distance}}{\text{speed}} = \frac{40 \,\text{km}}{8 \,\text{km/hr}} = 5 \,\text{hours}\)
\(t_{\text{total}} = t_{\text{downstream}} + t_{\text{upstream}} = 2.5 \,\text{hours} + 5 \,\text{hours} = 7.5 \,\text{hours}\)
Therefore, the total time taken for the boat to cover the entire journey, both upstream and downstream, is 7.5 hours.
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