Answer:
The current of the river has a speed of 3 miles per hour
Step-by-step explanation:
Let's call v the speed of the boat in calm waters.
We know that:
[tex]v = \frac{d}{t}[/tex]
Where d is the distance in miles and t is the time
When the boat travels down we have to:
[tex]d=2.4\ miles[/tex]
If s is the speed at which the boat travels downstream and c is the speed of the river then
[tex]s=(v+c)[/tex]
And
[tex]t=\frac{d}{s}\\\\t=\frac{d}{v+c}\\\\t=\frac{2.4}{21+c}[/tex]
When the boat travels upstream we have to:
[tex]d=1.8\ miles[/tex]
[tex]s=(v-c)[/tex]
[tex]t=\frac{d}{s}\\\\t=\frac{d}{v-c}\\\\t=\frac{1.8}{21-c}[/tex]
We know that the time he navigate upstream is the same time he navigate downstream
Then:
[tex]\frac{2.4}{21+c}=\frac{1.8}{21-c}[/tex]
We solve the equation for c
[tex]2.4*(21-c)=(21+c)*1.8[/tex]
[tex]50.4-2.4c=37.8+1.8c[/tex]
[tex]50.4-37.8=1.8c+2.4c[/tex]
[tex]4.2c=12.6[/tex]
[tex]c=\frac{12.6}{4.2}[/tex]
[tex]c=3\ miles\ per\ hour[/tex]
