Problema Solution
It takes a motor boat 32 hours to go downstream and 48 hours to go
upstream. How long does it take for an unpowered raft to cover this distance?
Answer provided by our tutors
Let
t1 = 32 hours downstream travel
t2 = 48 hours upstream travel
d = the distance traveled
v = the speed of the boat
x = the speed of the current
t = the time that the unpowered raft needs
t = d/w
the speed upstream is: v - x
the speed downstream is: v + x
since speed = distance/time => distance = speed * time
d/(v + w) = 32
d = 32v + 32w
d/w = 32v/w + 32 multiply both sides by 3
3(d/w) = 96 v/w + 96
d/(v - w) = 48
d = 48(v - w)
d/w = 48v/w - 48 multiply both sides by -2
-2d/w = - 96v/w + 96
3(d/w) - 2(d/w) = 96 v/w + 96 - 96v/w + 96
d/w = 192 hr
The unpowered raft will need 192 hours to cover the distance.