A Boat takes 10/3 hours to travel 30 km upstream and takes two hours to return the same distance downstream find the speed of the boat in still water and the speed of the stream
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Let the speed of the boat in still water be u and speed of the stream be v.
The speed while going upstream is u−v and going downstream is u+v.
We know that Time=
Speed
Distance
, hence we write the following equations:
u−v
30
+
u+v
44
=10
u−v
40
+
u+v
55
=13
Let u−v=x and u+v=y, the equations become,
x
30
+
y
44
=10 ........ (1)
x
40
+
y
55
=13 ........ (2)
Using 3×equation(2)−4×equation(1), we get:
y
165
−
y
176
=39−40
We get y=11.
Substituting the value in (1), we get x=5. Hence u+v=11 and u−v=5.
Therefore, speed of the boat in still water u=8km/h and speed of the stream is v=3km/h.
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