Question

A boat whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Answer 1

Let's assemble the equations to determine the velocity of the flow.
The boat makes the first trip downstream (descending, so the speed adds up). We can calculate the time by:
t = d / v

Remembering that we will need to add boat and river speeds in the first part: t = 30 / (15 + v)

In the second moment the boat is coming back, so to determine the time, we will need to subtract:
tb = 30 / (15-v)
We know that the total time of the trip was 4.5 hours, so: t, + t ,,, = 4.5
Riding the equation and solving:
900 = (15²-v²) * 4.5
15²-v² = 900 / 4.5
-v² = 200-225
v = √ 25
v = 5 km / h

The flow velocity is 5 km / h.