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# current

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a boat took 4 hours to make a trip downstream with a current of 6 km/h

the return trip against the same current took 10 hours

how far did the boat travel?

how do you find the solution?

Jun 27, 2018

#1
+106536
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Call the rate of the boat in still water, R

And when the boat is traveling with the current, its rate is  (R + 6)  km/ hr

So...  Rate  * Time  = Total Distance

( R + 6 ) * 4   =  D    (1)

And Distance  / Rate    = Time  (in hours)

Note that when the boat goes against the current, that its rate   is being slowed by the current...so its rate  is (R - 6)...so we have

D / ( R - 6)  =  10     (2)

Sub  (1)  into  (2)

(R + 6) * 4  / (R - 6)   =  10    simplify

(R + 6) * 4  =  10 (R - 6)

4R + 24  =  10 R - 60        subtract 4R  from both sides, add 60 to both sides

84  =  6R      divide both sides by  6

14  =  R     ( the rate in still water is 14 km/hr)

To find the distance, plug 14  into  (1)

(14 + 6) * 4   =  D

20 * 4  =  80

So...the distance is 80 km  (one way)

Jun 27, 2018
#2
+1

Let the boat's speed = S
Let the distance travelled = D  [one way]
D =Speed x Time
4[S + 6] = 10[S - 6], solve for S. Distance travelled downstream = Distance travelled upstream
S = 14 kp/h - the boat's speed
D =4[14 + 6] = 80 km - distance that the boat travelled[One Way].

Jun 27, 2018