Math word problems help please?

Question

f his owrkout, he reduced his speed by 5 miles per hour. Each portion of the workout took the same time. 

a.) the cyclist's speed during the first portion (in mph) 

b.)find his speed during the cool down portion (in mph). 

2.) A human factors expert recommends that there be at least 9 square feet of floor space in a college classroom for every student in the class. Find the minimum floor space that 84 students require. 

3.) To mix weed killer with water correctly, it is necessary to mix 15 teaspoons of weed killer with 5 gallons of water. Find how many gallons of water are needed to mix with the entire box if it contains 24 teaspoons of weed killer.

Answer 1

(1)

A cyclist ride the first 20 mile portion of his workout at a constant speed.
For the 16 mile cool down portion of his workout, he reduced his speed by 5 miles per hour.
Each portion of the workout took the same time.

(a)

For first portion :

The distance travelled in first portion is 20 mile .

Let the constant speed is s .

So the time taken for first portion of his workout is t = 20 / s .

For cool down portion :

The distance travelled in first portion is 16 mile .

Let the constant speed is s-5 .

So the time taken for first portion of his workout is t = 16 / s-5 .

Given that the time taken for each portion is same .

So 20/s = 16/s-5 

20(s-5) = 16s

20s - 100 = 16s

20s - 16s = 100

4s = 100

s = 100/4

s = 25

So the cyclist's speed during the first portion is 25 mph .

 

Answer 2

1(b)

For first portion :

The distance travelled in first portion is 20 mile .

Let the constant speed is s .

So the time taken for first portion of his workout is t = 20 / s .

For cool down portion :

The distance travelled in first portion is 16 mile .

Let the constant speed is s-5 .

So the time taken for first portion of his workout is t = 16 / s-5 .

Given that the time taken for each portion is same .

So 20/s = 16/s-5 

20(s-5) = 16s

20s - 100 = 16s

20s - 16s = 100

4s = 100

s = 100/4

s = 25

So the cyclist's speed during the first portion is 25 mph .

speed of cyclist during the cool down portion is 25 - 5 = 20 mph .

Answer 3

(2)

A human factors expert recommends that there be at least 9 square feet of floor space for every student .

So the minimum floor space  require for 84 students is  9*84 

                                                                                        = 756 .

The minimum floor space  require for 84 students is 756 square feet .

Answer 4

(3)

To prepare weed killer it is necessary to mix 15 teaspoons  of weed for 5 gallons of water .

Let the amount of water require for 24 tea spoons of weed is x .

Using the properties of ratio's , their ratio's should be equal 

5 gallons / 15 teaspoons  =  x gallons / 24 teaspoons 

 x gallons  = (5 gallons / 15 teaspoons ) * 24 teaspoons 

x gallons  = ( gallons / 3 teaspoons ) * 24 teaspoons 

x gallons  = (1/3)*24  gallons 

x gallons  = 8  gallons 

So the amount of water require for 24 tea spoons of weed is 8  gallons .