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okay, this problem has been really frustrating for me. I don't get it at all, so can someone please clearly explain to me how to get the answer?

-A boat travels 16 km downstream in 2 hours. It then travels the same distance upstream in 8 hours. Find the speed of the boat in still water and the speed of the current.

2007-01-21 12:11:14 · 5 answers · asked by Carley 3 in Science & Mathematics Mathematics

5 answers

let Sb = speed of boat
Sc = speed of current

*in going downstream, the speed of the current adds up to that of the boat. and opposite happens in going upstream.

so..
*total speed downstream = Sb + Sc
*total speed up stream = Sb - Sc

using distance = speed x time

16 = (Sb + Sc) x 2 -> downstream
8 = Sb + Sc
Sb = 8 - Sc (1)


16 = (Sb - Sc) x 8 -> upstream
2 = Sb -Sc (2)

*substituting (1) to (2),
2 = 8 - Sc - Sc
-6 = -2Sc

Sc = 3 km/hr
Sb = 8 - 3 = 5km/hr

ANSWER

Speed of boat = 5km/hr
Speed of current = 3km/hr

2007-01-21 13:45:30 · answer #1 · answered by swas77 2 · 0 0

Alright. Speed is distance over time, so when the boat is going downstream, it is travelling at 8km/h. Upstream, it is travelling at 2km/hr.

In each case, the speed of the boat (in still water) plus the speed of the current must equal the speed that it ends up travelling. So, let B be the speed of the boat in still water, and let C be the speed of the current.

Downstream: B + C = 8 (adding because the boat and the current are going in the same direction)

Upstream: B - C = 2 (subtracting because the current is now working against the boat)

If I rearrange the first equation to say "B = 8 - C", I can then put 8 - C into the second equation where B is. This makes it 8 - C - C = 2

This rearranges to 8 - 2 = 2C, or 6 = 2C, so C (the current) is 3 (km/h).

Substituting this value into either of the initial equations allows you to see that B (the speed of the boat in still water) is 5 (km/h).

Phew!

2007-01-21 20:28:47 · answer #2 · answered by Ben C 2 · 0 0

Let's say the speed of the boat in still waters is x, and the speed of the river flow is r. The distance travelled one way is 16 km. We have the following:

(x + r) 2 = 16
(x - r) 8 = 16 (because it's going UP stream!)

So we have:

2x + 2r = 16
x + r = 8
8x - 8r = 16
x - r = 2
2x = 10
x = 5
r = 3

2007-01-21 20:21:11 · answer #3 · answered by Scythian1950 7 · 0 0

Downstream, the speed of the boat and the current added is 8km/h
b + c = 8
Upstream, the speed of the boat against the current is 2km/h
b - c = 2

Using those two equations
2b = 10
b = 5
c = 8 - 5 = 3

The speed of the boat in still water is 5km/h
The speed of the current is 3km/h

2007-01-21 20:21:24 · answer #4 · answered by Tom :: Athier than Thou 6 · 0 0

Ask your teacher. Do your own homework.

y = mx + b

2007-01-21 20:19:26 · answer #5 · answered by Anonymous · 0 1

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