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

Answer:

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

Step-by-step 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:

$\displaystyle B-S=\frac{172}{3}$

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:

$\displaystyle B+S=\frac{372}{4}=93$

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:

$S = \frac{107}{6}\approx 17.83\ km/h$

From [2]:

$B = 93 - \frac{107}{6}$

$B=\frac{451}{6}\approx 75.17\ km/h$