Answer:
Since Peter's boat goes 4 times as fast as the current of the river:
Let the rate of the river current be c
Let the speed of Peter's boat be p
p = 4c
Peter took a trip 15 miles up the river
Distance traveled up the river = 15 miles
The speed up the river = 4c - c = 3c
Speed = Distance /time
3c = 15 / t
t = 15/3c
t = 5/c
The trip up the river lasted a period of 5/c hours
He came back after traveling up the river:
The speed down the river = 4c + c = 5c
Note that the distance down is still 15 miles
5c = 15/t
t = 15/5c
t = 3/c
The return trip lasted 3/c hours
The entire trip lasted 4 hours
Trip up the river + Return trip = 4
(5/c) + (3/c) = 4
8/c = 4
8 = 4c
c = 8/4
c = 2
Therefore, the rate of the river's current = 2 mph