# 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?

Relevance
• 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.

• 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.

• 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

CHECK

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

• 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

• 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.

• 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.

• 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

:)>

• 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.