The speed of boat is 10 km/hr in still water and speed of current is 4 km/hr. A man covered 12 km upstream, took some rest and then covered 14 km downstream. Find the period of time for which he took rest if he took 4 hrs to cover his complete journey.
The speed of boat is 10 km/hr in still water and speed of current is 4 km/hr. A man covered 12 km upstream, took some rest and then covered 14 km downstream. Find the period of time for which he took rest if he took 4 hrs to cover his complete journey.
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Given:
– Speed of the boat in still water = 10 km/hr
– Speed of the current = 4 km/hr
– Distance covered upstream = 12 km
– Distance covered downstream = 14 km
– Total time for the journey = 4 hrs
1. Calculate the downstream speed:
\[ \text{Downstream speed} = \text{Speed of boat in still water} + \text{Speed of current} \]
\[ \text{Downstream speed} = 10 + 4 = 14 \text{ km/hr} \]
2. Calculate the upstream speed:
\[ \text{Upstream speed} = \text{Speed of boat in still water} – \text{Speed of current} \]
\[ \text{Upstream speed} = 10 – 4 = 6 \text{ km/hr} \]
3. Calculate the time taken to cover 12 km upstream:
\[ \text{Time upstream} = \frac{\text{Distance upstream}}{\text{Upstream speed}} \]
\[ \text{Time upstream} = \frac{12}{6} = 2 \text{ hrs} \]
4. Calculate the time taken to cover 14 km downstream:
\[ \text{Time downstream} = \frac{\text{Distance downstream}}{\text{Downstream speed}} \]
\[ \text{Time downstream} = \frac{14}{14} = 1 \text{ hr} \]
5. Calculate the time for which he took rest:
\[ \text{Time for rest} = \text{Total time} – (\text{Time upstream} + \text{Time downstream}) \]
\[ \text{Time for rest} = 4 – (2 + 1) = 1 \text{ hr} \]
Conclusion:
The period of time for which he took rest is 1 hour.