## Answer :

And even though you haven't asked to be shown how to do it,

I'll go ahead and do that too:

Call the speed of the boat (through the water) 'B'.

Call the speed of the current (the water) 'C'.

When the boat is going 'up' the river,

*against*the current,

his speed past the riverbank is (B - C).

When the boat is going 'down' the river, the same way as the current,

his speed past the riverbank is (B + C).

The problem says it took him 5 hours to travel 60 km against the current.

Distance = (speed) x (time)

60 km = (B - C) x (5 hours)

The problem also says it took him 3 hours to return.

The distance to return is the same 60 km.

The other direction is the same direction as the current,

so his speed on the return is (B + C).

Distance = (speed) x (time)

60 = (B + C) x (3)

Now we have two equations, so we can find 'B' and 'C'.

5B - 5C = 60

3B + 3C = 60

Multiply each side of the first equation by 3, and

multiply each side of the second equation by 5:

**15B - 15C = 180**

**15B + 15C = 300**

*Add*the second equation to the first one:

30B = 480

B = 480/30 = 16 km per hour.

*Subtract*the second equation from the first one:

-30C = -120

C = -120/-30 = 4 km per hour.

**The speed of the boat through the water (B) is 16 km per hour.**

**The speed of the water past the riverbank is 4 km per hour.**

Check:

-- When the boat is going along with the current, his speed past the riverbank

is (16 + 4) = 20 km per hour. In 3 hours, he covers (3 x 20) = 60.

-- When the boat is going against the current, his speed past the riverbank

is (16 - 4) = 12 km per hour. In 5 hours, he covers (5 x 12) = 60 km.

yay !