Skip and Laurie paddle a raft 15 miles downstream in 3 hours

Skip and Laurie paddle a raft 15 miles downstream in 3 hours. On the return trip, they paddle the raft the same distance upstream in 5 hours. Find the rate of the current.

Solution

Let x=rate of raft
And y=rate of current

distance(d)=rate(r) times time(t) or d=rt and r=d/t
rate upstream: x-y=15/5=3mph
rate downstream: x+y=15/3=5mph
So our equations to solve are:
x-y=3-----------------eq 1
x+y=5---------------------eq 2
add eq 2 and eq 1
2x=8 divide both sides by 2
x=4 mph ---------------rate of raft
substitute x=4 into eq 2
4+y=5 subtract 4 from both sides
y=1 mph -------------rate of current