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A boat traveled 147 miles downstream and back. The trip downstream took 7 hours. The trip back took 21 hours. What is the speed

zimovet [89]

Answer:

The speed of current is 7 miles per hour

Step-by-step explanation:

Given as :

The distance cover by boat in downstream = D = 147 miles

The distance cover by boat in upstream = d = 147 miles

The time taken in downstream trip = T = 7 hours

The time taken in upstream trip = t = 21 hours

Let The speed of boat in still water = x mi/h

And The speed of current = y mi/h

The speed in downstream = S = (x + y) mi/h

The speed in upstream = s = (x - y) mi/h

Now, According to question

∵ Distance = speed × time

For downstream

D = S × T

Or, 147 miles = (x + y) mi/h × 7 hours

i.e 7 (x + y) = 147

Or, x + y = $\dfrac{147}{7}$

∴ x + y = 21 ........A

For upstream

d = s × t

Or, 147 miles = (x - y) mi/h × 21 hours

i.e 21 (x - y) = 147

Or, x - y = $\dfrac{147}{21}$

∴ x - y = 7 .......B

Now, Solving equations A and B

So, (x + y) + (x - y) = 21 + 7

Or, (x + x) + (y - y) = 28

Or, 2 x + 0 = 28

∴ x = $\dfrac{28}{2}$

i.e x = 14 miles per hour

The speed of boat in still water = x = 14 mi/h

Now, putting the value of x into eq B

So, y = x - 7

Or, y = 14 - 7

i.e y = 7 miles per hour

The speed of current = y = 7 mi/h

Hence, The speed of current is 7 miles per hour . Answer

7 0

3 years ago

Benjamin bought a 3- pound bag of flour for 6.95. What is the unit price per ounce of flour? (1 pound =16 ounces)

MrRissso [65]

Answer:

$0.145/ounce

Step-by-step explanation:

Find the unit price by dividing $6.95 by 3 pounds and then multiplying the result by (1 pound)/(16 oz):

$6.95 * 1 pound

------------------------------- = $0.145/ounce

(3 pounds) * (16 oz)

6 0

3 years ago

F(x) = x² +4x3 12 What is the vertex

Marat540 [252]

Step-by-step explanation:

We must take our equation and put it in vertex form,

f

(

x

)

=

a

(

x

−

h

)

2

+

k

where

h

,

k

is our vertex.

This equation will not factor into two squares

(

x

−

h

)

2

so we must use the completing the square method.

First we'll get rid of the

3

by subtracting it giving

x

2

−

4

x

=

−

3

Next we take half of the -4 the square it and add it to our equation to give us

x

2

−

4

x

+

4

. Since we added

4

to the left, we must also add it to the right giving

x

2

−

4

x

+

4

=

+

4

−

3

.

Now we can factor the left into two perfect squares,

(

x

−

2

)

2

=

1

.

Finally, we subtract

1

from both sides giving

(

x

−

2

)

2

−

1

. Our vertex is

h

,

k

giving

2

,

−

1

7 0

3 years ago

Mark's ratio is 3 tablespoons sugar to 2 tablespoons milk. Sharri is using 4 tablespoons of sugar to 3 tablespoons of milk. Eve

mezya [45]

Let's calculate for the tablespoons of sugar to tablespoons of milk ratio for Mark, Sharri and Eve.

Mark: 3/2 = 1.5
Sharri: 4/3 = 1.3
Eve: 9/6 = 1.5

From the solution, Eve has an equivalent ratio to that of Mark's.

4 0

3 years ago

Find the equation of a circle with center at (5, 6) and radius 8.

Elanso [62]

Answer:

(x - 5)^2 + (y - 6)^2 = 64

Step-by-step explanation:

Every circumference is in the form:

(x - xc)^2 + (y - yc)^2 = r^2

Where xc is the x of the center. Yc is the y of the center. r is the radius. We just plug in the values and we're done.

5 0

2 years ago

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