**Explanation :**Rate in still water=1/2(10+7)km/hr=8.5 km/hr.

Rate of current=1/2(10-7)km/hr=1.5 km/hr.

**Explanation :**rate downstream = (15/3 ¾)km/hr =(15*4/15)km/hr = 4km/hr.

Rate upstream =(5/2 ½)km/hr =(5*2/5)km/hr =2km/hr.

Speed of current = 1/2(4-2)km/hr = 1km/hr

**Explanation :**Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph.

So,2x=18 or x=9.

Rate upstream=9 km/hr,rate downstream=27 km/hr

Hence,rate of stream=1/2(27-9)km/hr=9 km/hr.

**Explanation :**Speed downstream =(7.5+1.5)km/hr=9 km/hr;

Speed upstream=(7.5-1.5)kmph=6kmph.

Let the required distance be x km.then, x/9+x/6=50/60.

2x+3x=(5/6*18)

5x=15 x=3.

Hence,the required distance is 3km

**Explanation :**let the speed of the motarboat in still water be x kmph.then, 6/x+2 +6/x-2=33/60

11x2-240x-44=0

11x2-242x+2x-44=0

(x-22)(11x+2)=0

x=22.

**Explanation :**let rate upstream=x km/hr and rate downstream=y km/hr.

Then,40/x +55/y =13…(i) and 30/x +44/y =10

Multiplying (ii) by 4 and (i) by 3 and subtracting ,we get:11/y=1 or y=11. Substituting y=11 in (i),we get:x=5.

Rate in still water =1/2(11+5)kmph=8kmph.

Rate of current=1/2(11-5)kmph=3kmph