Algebra: Show all work

Question

Michael can row a boat at an average speed of 12km/h in still water. Yesterday he rowed his boat on the river from home to another town. He rowed 32 kilometres down the river, and returned home. It took Eddie 6 hours for the whole trip. What is the rate of the river?

Answer 1

If the river's speed is r, then when he rowed with the current the combined speed was 12+r and when he rowed against the current it was 12-r. The time taken to row 32km downstream then upstream is 32/(12+r)+32/(12-r)=6, so 1/(12+r)+1/(12-r)=6/32; 24/(144-r^2)=6/32; 4/(144-r^2)=1/32; (144-r^2)/4=32; 144-r^2=128; r^2=16, so r=4kph.

Check: time to row with the current=32/16=2hrs; time to row against the current=32/8=4hrs; total time=6hrs.