Ask question

Ask question

All categories

4 years ago

11

A motorboat can go 8 miles downstream on a river in 20 minutes. It takes 30 minutes for the boat to go upstream the same 8 miles

. Find the speed of the current

2 answers:

ladessa [460]4 years ago

6 0

Answer:

<em>The speed of the current is </em><em>4 miles/hour</em>

Step-by-step explanation:

Let us assume that,

x = speed of the boat,

y = speed of the current.

We know that,

$\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$

A motorboat can go 8 miles <em>downstream</em> on a river in 20 minutes or $\dfrac{20}{60}$ hours.

$\Rightarrow x+y=\dfrac{8}{\frac{20}{60}}=\dfrac{8\times 60}{20}$

$\Rightarrow x+y=24$ --------------------------1

It takes 30 minutes for the boat to go <em>upstream</em> the same 8 miles.

$\Rightarrow x-y=\dfrac{8}{\frac{30}{60}}=\dfrac{8\times 60}{30}$

$\Rightarrow x-y=16$ ----------------------------2

Subtracting equation 1 and 2,

$\Rightarrow x+y-x+y=24-16$

$\Rightarrow 2y=8$

$\Rightarrow y=4$ miles/hour

sasho [114]4 years ago

3 0

4 miles per hour is the answer

You might be interested in

In triangle XYZ, angle Y = 45º and angle Z = 60º. If XZ = 4, then what is XY?

Katena32 [7]

Answer:

$XY = 4.9$

Step-by-step explanation:

Given

$XZ= 4$

$\angle Y = 45$

$\angle Z = 60$

Required

Determine the measure of side XY

To do this, we make use of sine law. This is as follows:

$\frac{a}{\sin\ A} = \frac{b}{\sin\ B} = \frac{c}{\sin\ C}$

In this case:

$\frac{4}{\sin(45)} = \frac{XY}{\sin(60)}$

Cross Multiply

$XY * \sin(45) = 4 * \sin(60)$

$XY * 0.7071 = 4 * 0.8660$

Make XY the subject

$XY = \frac{4 * 0.8660}{0.7071}$

$XY = \frac{3.4640}{0.7071}$

$XY = 4.89888276057$

$XY = 4.9$ -- <em>approximated</em>

3 0

3 years ago

Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same ro

nydimaria [60]

The key is Esther travelled the same distance - x - in both her morning and evening commute.

45(time she took in the morning, or p) = x
30(time she took in the evening, or q) = x

Therefore 45(p) = 30(q), or divide both sides by 5 and get 9(p) = 6(q). I know you can divide it further, but these numbers are small enough and it's not worth the time.

Since the whole trip took an hour, (p + q) = 60min, and so, p = 60-q.

Therefore 9(60-q) = 6q or 540-9q = 6q. So 540 = 15q, which makes q = 36. If q = 36, then by (p+q)=60, p (the time she took in the morning) must equal 24.

45 miles per hour, her speed in the morning, times (24/60) hours, her time, makes 18 miles travelled in the morning. If you check, 30 miles per hour times (36/60) hours also makes 18 miles in the evening.

<span>Hope that makes a little sense. And I also hope it's right</span>

7 0

3 years ago

Read 2 more answers

A plane takes off and flies at an angle of 11° with the ground. When it reaches an elevation of 500 ft, what is the distance flo

drek231 [11]

Answer:

It had flown 2620 ft along the diagonal.

Step-by-step explanation:

When the plane is taking off it forms we can form a triangle with it's height, horizontal distance and diagonal distance, which can be seen in the attached drawing. We can use the sine relation on the right triangle to determine "x", as shown below:

sin(11°) = 500/x

x*sin(11) = 500

x = 500/[sin(11)] = 2620 ft

It had flown 2620 ft along the diagonal.

7 0

3 years ago

if Paula wants the tops of the latter to reach exactly 8 feet up the building, what is x, the distance between the building and

cluponka [151]

Answer:

6 ft

Step-by-step explanation:

Since the distance between the bottom of the ladder and the wall forms a right angle that is across from the ladder, you can use the Pythagorean Theorem to solve for the value of 'x':

a² + b² = c², where 'a' and 'b' are the legs of the triangle and 'c' is the diagonal or hypotenuse.

Using 8 for 'a' and 10 for 'c':

8² + x² = 10²

64 + x² = 100

Subtract 64 from both sides:

64 - 64 + x² = 100 - 64 or x² = 36

Take the square root of both sides:

√x² = √36

x = 6 ft

5 0

4 years ago

Solve for x. 5x - 1 = 26 x = x = 5 x = -5

Doss [256]

Answer:

x = 27/5

Step-by-step explanation:

5x - 1 = 26

Add 1 to each side

5x - 1 = 26

5x-1+1 = 26+1

5x = 27

Divide each side by 5

5x/5 = 27/5

x = 27/5

5 0

3 years ago