A barge moves 6km/h in still water. It travels 51 km upriver and 51 km downriver in a total time of 114 hr. What is the speed of the current?

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A barge moves 6km/h in still water. It travels 51 km upriver and 51 km downriver in a total time of 114 hr. What is the speed of the current?

Mathematics
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Let x be the speed of the current, and \[t _{1}, t _{2}\] be the times to go up and downriver, respectively
Then \[(6+x)t _{1} + (6-x)t _{2} = 102\] and \[t _{1}+t _{2}=114\]
\[(6+x)t _{1}=51\] \[(6-x)t _{2}=51\] \[t _{1}=114-t _{2}\] Using these three equations and making substitutions I found the speed to be 5.1km/hr

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I'm actually still not too sure i understand this, but I thank you for your fast response. I'll just look at it a bit longer and hopefully I'll get it.
it seems everyone does this problem a different, but i'll figure it out eventually.

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