29 Jun, 2021 08:07 PM

The speed of a stream is 4mph. A boat travels 8 miles upstream in the same time?

it takes to travel 16 miles downstream.What is the speed of the boat in still water? The speed is __mph.

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Answer
MA
29 Jun, 2021 08:07 PM

Distance = Velocity * time

let

b = speed of boat in still water

Upstream

8 = (b - 4)t

Downstream

16 = (b + 4)t

Double the Upstream equation

16 = 2(b - 4)t

Since both equations equal 16 set them equal

(b + 4)t = 2(b - 4)t

Divide both sides by t

b + 4 = 2(b - 4)

b + 4 = 2b - 8

Subtract b from both sides

4 = b - 8

Add 8 to both sides

12 = b

The speed is 12 mph

m07202013

DA
29 Jun, 2021 08:08 PM

4 mph is the speed of the stream.  That means is the stream affects the boat 4 mph in both directions.  (That's 8 mph total.) The boat goes a total of 8 actual + 4 against the stream upstream = 12 mph.

And it goes 16 actual -  4 with the stream downstream = 12 mph

Note: it must be one hour because the difference is 8 miles    

So The speed is 12 mph