Answer:
5 km/hr
Step-by-step explanation:
You want the speed of the current if a ship traveled 120 km and back in 5 hr 24 min, and its speed in still water is 45 km/hr.
Time
The relationship between time, speed, and distance is ...
t = d/s
Where c is the speed of the current, the total time for the trip and return is ...
[tex]5.4=\dfrac{120}{45+c}+\dfrac{120}{45-c}[/tex]
Solution
Multiplying by the product of the denominators, we have
[tex]5.4(45+c)(45-c)=120(45-c)+120(45+c)\\\\45^2-c^2=2000\qquad\text{simplify, divide by 5.4}\\\\25=c^2\qquad\text{add $c^2-2000$}\\\\c=5\qquad\text{positive square root}[/tex]
The speed of the current is 5 km/hr.
