Let speed of stream be xkm∕h. Speed of boat downstream =(30+x)km∕h Speed of boat upstream =(30−x)km∕h Distance travelled downstream =60km Distance travelled upstream =60km Time taken by boat in upstream =
distance travelled upstream
Speed upstream
=
60
(30−x)
Time taken by boat in downstream =
distance travelled downstream
Speed downstream
=
60
30+x
Total time taken =
9
2
h
9
2
=
60
30−x
+
60
30+x
⇒
9
2
=
60(30+x)+60(30−x)
900−x2
⇒
9
2
=
3600
900−x2
⇒
1
2
=
400
900−x2
⇒900−x2=800 ⇒x2=100 ⇒x=10km∕h Hence, the speed of the stream is 10km∕h.