Question

A boat took 2 hours to travel a certain distance upstream against a 3 km/h current.

Returning downstream with the same current, the boat travelled an additional 2 km
in one hour and 20 minutes. What was the boat's speed in still water? How far did
the boat go upstream?

Answer 1

The speed in still water is 12 km/h.

The upstream distance is 20 km.

Explanation:

speed of boat in still water = s

speed of current = 3 km/h

speed of boat upstream = s - 3

speed of boat downstream = s + 3

distance upstream = d

distance downstream = d + 2

time upstream = 2 hours

time downstream = 1 h 20 m = 1 1/3 h = 4/3 h

speed = distance/time

distance = speed × time

Upstream:

distance = speed × time

d = (s - 3) × (2)

d = 2s - 6 Eq. 1

Downstream:

distance = speed × time

d + 2 = (s + 3) × (4/3)

3d + 6 = 4s + 12

3d - 4s = 6 Eq. 2

Equations 1 and 2 form a system of equations:

d = 2s - 6

3d - 4s = 6

3(2s - 6) - 4s = 6

6s - 18 - 4s = 6

2s = 24

s = 12

d + 2 = (s + 3)(4/3) = (15)(4/3) = 20

The speed in still water is 12 km/h.

The upstream distance is 20 km.