Question

Jane took 20 min to drive her boat upstream to​ water-ski at her favorite spot. Coming back later in the​ day at the same boat​ speed took her 10 min. If the current in that part of the river is 4 km per​ hr, what was her boat speed in still​ water?

Answer 1

12 km/hour

Explanation:

Given information: The current in that part of the river is 4 km per​ hr.

Speed of current = 4 km per hour

Let x be the speed of boat in still​ water.

Speed of boat in upstream = x-4 km per hour

Speed of boat in downstream = x+4 km per hour

Assume that the distance between Jane's initial position and Jane's favorite spot is D.

Jane took 20 min to drive her boat upstream to​ water-ski at her favorite spot.

`Distance=Speed* Time`

For upstream,

`Distance=(x-4)* 20`

`Distance=20x-80` .... (1)

For downstream,

`Distance=(x+4)* 10`

`Distance=10x+40` ..... (2)

Equate (1) and (2) we get

`20x-80=10x+40`

Isolate variable terms.

`20x-10x=80+40`

`10x=120`

Divide both sides by 10.

`x=12`

The value of x is 12. Therefore, the speed of boat in still water is 12 km/hour.

Answer 2

(x-5)*20 = d
coming downstream:
(x+5)*15 = d
since both equations equal d, then they are equal to each other, so:
(x-5)*20 = (x+5)*15
expanding, this becomes:
20*x - 100 = 15*x + 75
subtract 15*x from both sides and add 100 to both sides to get:
20*x - 15*x = 75 + 100
which becomes:
5*x = 175


divide both sides by 5 to get:
x = 35 miles per hour
this means that the boat's speed is 35 miles per hour.
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to prove this is correct, substitute in the original equation of:
(x-5)*20 = (x+5)*15
which becomes:
(35-5)*20 = (35+5)*15
which becomes:
30*20 = 40*15
divide both sides by 15 to get:
30/15*20 = 40
which becomes:
2*20 = 40
which is true so the values for the boat speed are good.
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