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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?

Sagot :

elcharly64

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:

[tex]\displaystyle B-S=\frac{172}{3}[/tex]

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:

[tex]\displaystyle B+S=\frac{372}{4}=93[/tex]

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:

[tex]S = \frac{107}{6}\approx 17.83\ km/h[/tex]

From [2]:

[tex]B = 93 - \frac{107}{6}[/tex]

[tex]B=\frac{451}{6}\approx 75.17\ km/h[/tex]

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