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# i dont get this help?

The speed of a stream is 3 mph. A boat travels 11 miles upstream in the same time it takes to travel 17 miles downstream. What is the speed of the boat in still water?

### 8 Answers

- PinkgreenLv 72 months ago
Let v mph be the speed of the boat in still water.

17/(v+3)=11/(v-3)

=>

17(v-3)=11(v+3)

=>

17v-51=11v+33

=>

6v=84

=>

v=14 mph.

- PhilipLv 62 months ago
d = rt. distance = rate*time. Stream rate = 3 mi/h. Put boat's rate in still water = bmi/h

Against the stream: d =11 mi, r = (b-3) mi/h, t against stream = ta = [11mi/(b-3)](h/mi).

With the stream: d = 17 mi, r = (b+3) mi/h, t with stream = tw = [17mi/(b+3)](h/mi).;

Now ta = tw. ie., 11/(b-3) = 17/(b+3),ie., 11(b+3) = 17(b-3), ie., 33+51= 6b, ie., b =14.

Boat's rate in still water = 14 mi/h.

- ranjankarLv 72 months ago
LET THE SPEED IN STILL WATERS BE X

UPSTREAM SPEED = X-3 mph

DOWNSTREAM SPEED = X+3 mph

TIME TAKEN = 11/ (X-3) = 17/ (X+3)

CROSS MULTIPLY

17X-51 = 11X+33

6X= 84

X = 14 mph ANSWER

CHECK

11/ (14-3) = 17/ ( 14+3) = 1 HOUR

- la consoleLv 72 months ago
Recall: s = d/t → where s is the speed, d is the distance, t is the time

Sb: speed of the boat

Sc: speed of the current = 3 mph

The case downstream (17 miles).

The speed of the boat and the speed of the current are in the same direction.

You can add these speeds together.

s = d/t

Sb + Sc = d/t → where: d = 17 miles and where: Sc = 3 mph

Sb + 3 = 17/t

t = 17/(Sb + 3)

The case upstream (11 miles).

The speed of the boat and the speed of the current are opposite, so you make the difference.

s = d/t

Sb - Sc = d/t → where: d = 11 m and where: Sc = 3 mph

Sb - 3 = 11/t

t = 11/(Sb - 3) → given that the time is the same → recall: t = 17/(Sb + 3)

11/(Sb - 3) = 17/(Sb + 3)

11.(Sb + 3) = 17.(Sb - 3)

11Sb + 33 = 17Sb - 51

- 6Sb = - 84

Sb = 14 mph ← this is the speed of the boat in still water

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- KrishnamurthyLv 72 months ago
The speed of a stream is 3 mph.

A boat travels 11 miles upstream in the same time

it takes to travel 17 miles downstream.

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

11/(x - 3) = 17/(x + 3)

11(x + 3) = 17(x - 3)

6x = 33 + 51

x = 84/6 = 14

The speed of the boat in still water is 14 mph.

- sepiaLv 72 months ago
The speed of a stream is 3 mph.

A boat travels 11 miles upstream in

the same time it takes to travel 17 miles downstream.

What is the speed of the boat in still water?

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

As the speed of the stream is 3 mph,

upstream speed will be ( x − 3) mph

and downstream speed will be (x + 3) mph.

The time taken by the boat for traveling 11 miles upstream will be 11/x − 3

and time taken by the boat for traveling 17 miles downstream is 17/x + 3.

As the two are equal 11/(x − 3) = 17/x + 3

Hence

17(x - 3) = 11(x + 3).

6x = 84

Hence x = 14.

- Wayne DeguManLv 72 months ago
Let the speed of the boat be v m.p.h

Against the stream we have:

(v - 3)t = 11

With the stream we have:

(v + 3)t = 17

so, 11/(v - 3) = 17/(v + 3)

=> 11(v + 3) = 17(v - 3)

i.e. 11v + 33 = 17v - 51

so, 6v = 84

Hence, v = 14 m.p.h

Then, (14 - 3)t = 11

i.e. t = 1 hour

Total journey 2 hours

:)>

- vaklasLv 42 months ago
This should be in the Physics Section but once again it is proven that maths are behind everything.

Assume that the boat in still water travels with speed v mph. If it travels downstream, it takes advantage on the speed of the stream and travels with v + 3 mph. If it travels upstream it loses some speed from the opposite direction of the stream, hence v - 3 mph.

Since v + 3 = 17, and v - 3 = 11, you can see that the speed of the boat in still water (if the stream speed was 0) would be 14 mph.