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

1.8 mph

Explanation:

Answer 2

1.8 mph

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(2)/(3)=(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)((11)/(3))`

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

`(18+c)(3)=(18-c)((11)/(3))\\54+3c=(198)/(3)-(11)/(3)c\\3c+(11)/(3)c=(198)/(3)-54\\(20)/(3)c=12\\c=(12)/((20)/(3))\\c=12*(3)/(20)=1.8`

Thus, speed of current = 1.8 mph