Question

a boat on the Potomac river travels the same distance downstream with current in 2/3 hr as it does going upstream against the current in 1hr. if the speed of the current is 3 mph, find the speed of the boat in still water.

Answer 1

Answer: 15 mph

1) Name the variables:

Vd: net velocity downstream
Vu: net velocity upstream
Vc: velocity of the current = 3 mph
Vb: velocity of the boat in still water
x: distance

2) Downstream the net velocity is the velocity of the boat in still water plus the velocity of the current.

=> Vd = Vb + 3

3) Upstream the net velocity is the velocity of the boat in still water less the velocity of the current.

=> Vu = Vb - 3

4) time of the trip downstream = 2/3 h

=> Vd = x / (2/3 = Vb + 3

5) time of the trip upstream - 1 h

=> Vu = x / 1 = Vb - 3

6) Solve the system of equations:

Vb + 3 = x /(2/3)
Vb - 3 = x

subract the second equation from the first:

Vb + 3 - Vb - (-3) = x/(2/3) - x
3 + 3 = 3x/2 - x
6 = x/2

x = 12 miles

7) Replace x = 12 miles on any of the equations:

Vb - 3 = x

Vb = 12 + 3 = 5

Vb = 15 mph