Math homework help mayne?

Question

1. A boat is going 32 miles downstream in two hours. THe return trip against the current takes 16 hours. Find the rate of the boat in calm water and the rate of the current.

2. In a naval engagement 1/3 of the fleet was captured, 1/6 sunk and two ships were burned; 1/7 of the remainder was lost in a storm after the battle. FInally, 24 ships sailed home. How many ships were in the fleet before the engagement.

3. The volume of a cylinder is 600pi centimeters cubed. The daius of a base of the cylinder is 5 cm. What is the height of the cylinder?

4. New tile is being laid in a room 40 feet long by 22 feet wide. If each square tile is 6 inches x 6 inches, how many tiles will be needed to cover the floor.

Answer 1

1.

A boat is going 32 miles downstream in two hours.

The return trip against the current takes 16 hours.

Find the rate of the boat in calm water

and the rate of the current.

32/(x + c) = 2

32/(x - c) = 16

x + c = 16

x - c = 2

x = 9

c = 7

The speed of the boat is 9 mph and the speed of the current is 7 mph.



2.

In a naval engagement 1/3 of the fleet was captured,

1/6 sunk and two ships were burned;

1/7 of the remainder was lost in a storm after the battle.

Finally, 24 ships sailed home.

[x - (x/3 + x/6 + 2)] = (x - 4)/2

(6/7)(x - 4)/2 = 24

x = 60

60 ships were in the fleet before the engagement.



3.

The volume of a cylinder is 600 pi centimeters cubed.

The radius of a base of the cylinder is 5 cm.

What is the height of the cylinder?

V = pi r^2 h

h pi 25 = 600 pi

h = 24 cm



4.

New tile is being laid in a room 40 feet long by 22 feet wide.

If each square tile is 6 inches x 6 inches,

how many tiles will be needed to cover the floor?

3,520 tiles are needed to cover the floor.

Answer 2

1)

x = speed of boat in calm water

c = rate of current



32 / (x + c) = 2

2x+2c = 32

x+ c = 16



32 /(x-c) = 16

16x-16c = 32

x-c = 2



x+c = 16

x- c = 2

add:

2x=18

x = 9 miles per hour (speed of boat)

9+c = 16

c = 7

c = 7 miles per hour (rate of current)



2)

Let there be x ships

Captured = x/3

sunk = x/6

burned = 2

x/3+x/6+2+ (1/7)( x-x/3-x/6-2) = 24

x/3 + x/6 + 2 +x/7 - x/21 -x/42 - 2/7 = 24



Multiply both sides by 42

14x+7x+84+6x-2x-x-12 = 1008

x= 39 ships before engagement





3)

Volume = pi r^2 h = 600 pi

r^2 h = 600

(5)^2 h = 600

25 h = 600

h = 24 cm



4)

Total area = 40 x 22 = 880 ft^2

6 in = 0.5 feet

each tile is .5 x .5 = .25 ft^2

number of needed tiles = 880 / 0.25 = 3,520

Answer 3

6(f-f/3-f/6-2)/7=24



(f-f/3-f/6-2)=28



f-f/3-f/6=30



6f-2f-f=180



3f=180



f=60



so there were sixty ships in the fleet before battle.



...



V=hpr^2 we are given V and r so



600p=25hp



h=600p/25p



h=24 cm



...



since six inch tiles fit neatly in both the width and length...we will just use inches for units...



(40*12*22*12)/36 the numerator is just; converted from square feet to square inches



so 1920 tiles will be needed in the room...