A boat covers a distance of $96 ext{ km}$ downstream in a time which is 25\% less than the time taken to cover the same distance upstream. If the boat covers $36 ext{ km}$ upstream in $1.5$ hours, find the speed of the boat in still water.

Question

A boat covers a distance of $96 	ext{ km}$ downstream in a time which is 25\% less than the time taken to cover the same distance upstream. If the boat covers $36 	ext{ km}$ upstream in $1.5$ hours, find the speed of the boat in still water.

Accepted Answer

**Solution:**

1. First, calculate the upstream speed of the boat. Given that the boat covers $36 	ext{ km}$ upstream in $1.5$ hours:
   
   $$	ext{Upstream speed} = \frac{36}{1.5} = 24 	ext{ km/hr}$$

2. Let the downstream speed be $d$ km/hr and the upstream speed be $u = 24$ km/hr.

3. The time taken to cover $96$ km upstream is:
   
   $$t_u = \frac{96}{u} = \frac{96}{24} = 4 	ext{ hours}$$

4. The time taken downstream is $25\%$ less than upstream time, so:
   
   $$t_d = t_u - 0.25 	imes t_u = 0.75 	imes 4 = 3 	ext{ hours}$$

5. Using downstream time, calculate downstream speed:
   
   $$d = \frac{96}{3} = 32 	ext{ km/hr}$$

6. Speed of boat in still water $b$ and speed of stream $s$ satisfy:
   
   $$d = b + s = 32$$
   $$u = b - s = 24$$

7. Adding the two equations:
   
   $$2b = 32 + 24 = 56 \implies b = 28 	ext{ km/hr}$$

**Answer:** $28 	ext{ km/hr}$

Answer

Answer

Answer

Answer