Question

A steamer going downstream traveled the distance between two ports in 3 hours. The return trip took 3 hours and 40 minutes. Find the speed of the water current if the speed of the steamer in still water is 18 MPH?

Answer 1

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  = $3\frac{2}{3}=\frac{11}{3}$ 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:

$D_{down}=D_{up}\\(x+c)t=(x-c)t\\(18+c)(3)=(18-c)(\frac{11}{3})$

Now, we solve this algebraically for "c", speed of current:

$(18+c)(3)=(18-c)(\frac{11}{3})\\54+3c=\frac{198}{3}-\frac{11}{3}c\\3c+\frac{11}{3}c=\frac{198}{3}-54\\\frac{20}{3}c=12\\c=\frac{12}{\frac{20}{3}}\\c=12*\frac{3}{20}=1.8$

Thus, speed of current = 1.8 mph