Question

A motorboat travels 172 km in 3 hours going upstream and 372 in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

The rate of the boat is 75.17 km/h and the rate of the stream is 17.83 km/h

Explanation:

System of Equations

Let's call:

B = speed (rate) of the boat in still water

S = speed (rate) of the stream

The boat travels 172 km in 3 hours when going upstream, that is when the speed of the stream subtracts its own speed. The speed is the distance divided by the time, thus:

`\displaystyle B-S=(172)/(3)`

Multiplying by 3:

3B - 3S = 172 [1]

The boat travels 372 km in 4 hours downstream when the speed of the current adds to its own:

`\displaystyle B+S=(372)/(4)=93`

B + S = 93

Solving for B:

B = 93 - S [2]

Substituting in [1]

3(93 - S) - 3S = 172

Operating:

279 - 3S - 3S = 172

279 - 6S = 172

Subtracting 279:

- 6S = 172 - 279

- 6S = -107

Multiplying by -1 and solving for S:

`S = (107)/(6)\approx 17.83\ km/h`

From [2]:

`B = 93 - (107)/(6)`

`B=(451)/(6)\approx 75.17\ km/h`