A boat covers $144 ext{ km}$ downstream in $8$ hours and $224 ext{ km}$ upstream in $16$ hours. Find the time taken by the boat to cover $128 ext{ km}$ in still water.

Question

A boat covers $144 	ext{ km}$ downstream in $8$ hours and $224 	ext{ km}$ upstream in $16$ hours. Find the time taken by the boat to cover $128 	ext{ km}$ in still water.

Accepted Answer

**Solution:**

1. Calculate the downstream speed:
   - Downstream speed = $\frac{	ext{Distance downstream}}{	ext{Time downstream}} = \frac{144}{8} = 18 	ext{ km/h}$

2. Calculate the upstream speed:
   - Upstream speed = $\frac{	ext{Distance upstream}}{	ext{Time upstream}} = \frac{224}{16} = 14 	ext{ km/h}$

3. Find the speed of the boat in still water:
   - Speed in still water = $\frac{	ext{Downstream speed} + 	ext{Upstream speed}}{2} = \frac{18 + 14}{2} = 16 	ext{ km/h}$

4. Calculate the time taken to cover $128 	ext{ km}$ in still water:
   - Time = $\frac{	ext{Distance}}{	ext{Speed}} = \frac{128}{16} = 8 	ext{ hours}$

**Answer:** $8 	ext{ hours}$

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