Question 159
a) Helena and Gabriel jump simultaneously from a raft into a river and swim in opposite directions. Gabriel swims downstream with the current and Helena swims upstream against the current, possibly at a different speed. After 5 minutes, they turn around and swim back to the raft, each keeping a constant speed the whole time. Who arrives first? (During this time, the raft was anchored, that is, it stayed still despite the current.)
b) At his usual speed, a man goes down a river $15~\mathrm{km}$ long in 5 hours less than the time he takes swimming the same river in the opposite direction. If he doubles his usual speed, he goes down the river taking only 1 hour less than the time spent on the way back. Assuming that the speed of the river current stays constant during the trips, what is its value in $\mathrm{km} / \mathrm{h}$?
b) At his usual speed, a man goes down a river $15~\mathrm{km}$ long in 5 hours less than the time he takes swimming the same river in the opposite direction. If he doubles his usual speed, he goes down the river taking only 1 hour less than the time spent on the way back. Assuming that the speed of the river current stays constant during the trips, what is its value in $\mathrm{km} / \mathrm{h}$?