Explanation :

Let the speed of the boat in still water be u kmph. Then, 

Downstream speed = (u + 3) kmph

Upstream speed = (u - 3) kmph

∴  (u + 3) x 1 = (u - 3) x $\dfrac{3}{2}$

⇒ 2u + 6 = 3u - 9 

⇒ u = 15 kmph

Explanation :

Downstream speed = (5 + 1) kmph = 6 kmph

Upstream speed = (5 - 1) kmph = 4 kmph

Let the required distance be x km.

∴ $\dfrac{\text{x}}{6} + \dfrac{\text{x}}{4} =1$

⇒ 10x = 24 

⇒ x = 2.4 km

Explanation :

Downstream rate = $\dfrac{1}{10}$ x 60 km/hr = 6 km/hr

Upstream rate = 2 km/hr

∴ Speed in still water = $\dfrac{1}{2}$(6 + 2) km/hr = 4 km/hr

Hence, required time taken = $\left(\dfrac{5}{4}\right)$ hr = 1 hr 15 min

Explanation :

Let the man’ rate upstream be a kmph and that downstream be b kmph. 

∴  Distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs

⇒ a x $\left( 8 + \dfrac{48}{60}\right)$ = b x 4

⇒ a x $\dfrac{44}{5}$ = 4b

⇒ b = $\left(\dfrac{44}{5}\right)$ a

Hence, required ratio

= $\dfrac{b+a}{2} : \cfrac{b-a}{2}$

= $\dfrac{\cfrac{11a}{5}+a}{2} : \dfrac{\dfrac{11a}{5}-a}{2} $

= $ \dfrac{16a}{10} : \dfrac{6a}{10}$

= 16 : 6

= 8 : 3

Explanation :

Let the rate of upstream be x kmph and rate of downstream be y kmph. Then,

$ \dfrac{24}{\text{x}} + \dfrac{36}{\text{y}}= 6 ---(1) \\  \dfrac{36}{\text{x}} + \dfrac{24}{\text{y}}= \cfrac{13}{2} ---(2)$

Adding equation (1) and (2), then

$ \therefore 60\left(\dfrac{1}{\text{x}} + \dfrac{1}{\text{y}} \right)= \dfrac{25}{4} \\ \Rightarrow \dfrac{1}{\text{x}} + \dfrac{1}{\text{y}}= \dfrac{5}{24} ---(3)$

Subtracting equation (1) and (2), then

$ \therefore 12\left(\dfrac{1}{\text{x}} - \dfrac{1}{\text{y}}\right )= \dfrac{1}{2} \\ \Rightarrow \dfrac{1}{\text{x}} - \dfrac{1}{\text{y}}= \dfrac{1}{24} ---(4)$

Adding equation (3) and (4), then

$ \therefore \dfrac{2}{\text{x}}= \dfrac{6}{24} \\ \Rightarrow \text{x}=8$

Putting the value of x in equation(4), then

$ \therefore \dfrac{1}{8} - \dfrac{1}{\text{y}}= \dfrac{1}{24} \\ \Rightarrow \dfrac{1}{8} - \dfrac{1}{24}= \dfrac{1}{\text{y}} \\ \\ \Rightarrow \dfrac{2}{24} = \dfrac{1}{\text{y}} \\ \Rightarrow \text{y} =12 $

∴ Upstream speed = 8 kmph and Downstream speed = 12 kmph

Hence, Rate of current = $\dfrac{1}{2}$(12 - 8) kmph = 2 kmph