Question

A motorboat that travels with a speed of 20 km/hour in still water has traveled 36 km against the current and 22 km with the current, having spent 3 hours on the entire trip. Find the speed of the current of the river.

Answer 1

same d = rt

so the boat's still water speed is 20kph, if we... say the current of the river is "r", then, when the boat was going upstream, its speed was " 20 - r", and when it was going downstream, is " 20 + r", since the river's current is adding speed to it

again, if on the way up, it took "t" hours, on the way down, it took the slack of the 3hrs, or " 3 - t"

thus
`\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ upstream&36&20-r&t\\ downstream&22&20+r&3-t \end{array} \\\\\\ \begin{cases} 36=t(20-r)\implies (36)/(20-r)=\boxed{t}\\\\ 22=(20+r)(3-t)\\ ----------\\\\ 22=(20+r)\left( 3- \boxed{(36)/(20-r)}\right) \end{cases}`

solve for "r"