Question 404881
If the boat speed is x kmh, river speed is y kmh, then when boat go downsteram it speed is {{{(x+y)}}}, upstream speed is {{{(x-y)}}}
a boat takes 2 hours to go 30 km downstream, so downstream speed is {{{30/2=15}}} kmh, so {{{(x+y)=15}}}
a boat takes 3 hours to go 30 km upstream, so upstream speed is {{{30/3=10}}}kmh
so {{{(x-y)=10}}}
Equations system
{{{x+y=15}}}
{{{x-y=10}}}Add the first equation to the second
.
{{{2x=25}}}
{{{x=25/2}}}
{{{x=12.5}}} kmh is the boat speed
The river speed is {{{12.5+y=15}}} {{{y=15-12.5}}}  {{{y=2.5}}}kmh
Answer The boat speed is 12.5 kmh