Question 133076
rate of the current: r
downstream rate of the boat: 8 + r
upstream rate of the boat: 8 - r


distance = rate times time, or {{{d=rt}}}, so {{{t=d/r}}}.


Downstream trip:  {{{t=24/(8+r)}}}
Upstream trip: {{{t=8/(8-r)}}}


Since the times for each trip are equal:


{{{8/(8-r)=24/(8+r)}}}


Cross multiply:
{{{8(8+r)=24(8-r)}}}


Distribute:
{{{64+8r=192-24r}}}


Collect like terms:
{{{8r+24r=192-64}}}


{{{32r=128}}}


{{{r=4}}}


So the rate of the current is 4.


Check:
8mph + 4mph  = 12mph, 24m/12mph = 2 hr

8mph - 4mph = 4mph, 8m/4mph = 2 hr

Answer checks