Question

A boat goes downstream in a river and covers the distance between two ports in 4 hours. It covers the same distance upstream in 5 hours. If the speed of the river is 2 km/h, find the speed of the boat in still water. [km/h is kilometer per hour]

Answer 1

Where did you get stuck?

Answer 2

Do you have an idea about how to start?

Answer 3

nope

Answer 4

When going upward the boat takes a little longer than when going downward, right? That's is because is moving against the velocity of the river. And when going downward it takes less because the velocity of the river is helping it.

Answer 5

If the distance travelled is d, the mean velocity going upward is d/(5 hours) and when going downward the velocity is d/(4 hours).

Answer 6

If going upward the velocity of the river, vr, subtracts some of the total velocity of the boat, vb. An equation that expresses this relationship can be:

\(\large{v_b-v_r = \frac{d}{5\ hours}}\)

Answer 7

If downward the velocity of the river instead of subtracting is helping (adding) to the boat's velocity, an expression can be:

\(\large{v_b+v_r= \frac{d}{4\ hours}}\)

Answer 8

Fortunately, we know what \(v_r\) is. And you can also disregard the word 'hours' in the expressions. The you get:

\(\large{v_b-2 = \frac{d}{5}}\)

\(\large{v_b+2= \frac{d}{4}}\)

If you get rid of the fractions you will end up with 2 nice equations with 2 unknowns, and you just need to solve them as a system of equations.