Answer:
1.8 mph
Step-by-step explanation:
first, let's convert 3 hour 40 minutes into hours (to keep same units).
40 minutes is 40/60 = 2/3 hour
So 3 hr 40 minutes = [tex]3\frac{2}{3}=\frac{11}{3}[/tex] hours
Now, we know D = RT
where D is distance, R is rate, and T is time
Let rate of steamer be x (which is 18)
and rate of current be c
Rate Downstream = x + c (goes with current)
Rate Upstream = x - c (goes against current)
Both Distance (upstream & downstream) are same. Thus, we can write:
[tex]D_{down}=D_{up}\\(x+c)t=(x-c)t\\(18+c)(3)=(18-c)(\frac{11}{3})[/tex]
Now, we solve this algebraically for "c", speed of current:
[tex](18+c)(3)=(18-c)(\frac{11}{3})\\54+3c=\frac{198}{3}-\frac{11}{3}c\\3c+\frac{11}{3}c=\frac{198}{3}-54\\\frac{20}{3}c=12\\c=\frac{12}{\frac{20}{3}}\\c=12*\frac{3}{20}=1.8[/tex]
Thus, speed of current = 1.8 mph
