Let the speed of the motorboat in still water be x‌km∕h. Then, Downstream speed =(x+2)‌km∕h Upstream speed =(x−2)‌km∕h ∴
5
x+2
+
5
x−2
=
4
3
⇒
1
x+2
+
1
x−2
=
4
15
⇒
2x
x2−4
=
4
15
⇒4x2−30x−16=0 ⇒2x2−15x−8=0 ⇒2x2−16x+x−8=0 ⇒2x(x−8)+1(x−8)=0 ⇒(x−8)(2x+1)=0 ⇒x=8 [as x cannot be negative] Hence, speed of motorboat in still water = 8 km/h