two boats travel at the same speed to different destinations. boat a reaches its destination in 12 minutes. boat b reaches its destination in 18 minutes. boat b travels 3 miles farther. how fast do the boats travel?

Faster boat: 4 miles/hr; Slower boat: 3 miles/hr

Explanation:

Let the slower boat travel at  

x

miles/hr

∴

the faster boat travels at  

(

x

+

1

)

miles/hr

After 1 hour the slower boat has travelled  

x

miles

and the faster boat has travelled  

x

+

1

miles.

We are told that:

(i) the boats travel at right angles to each other and

(ii) after 1 hour the boats are 5 miles apart

Hence we can use Pythagoras on the right angle triangle formed by the path of both boats and the distance between them as follows:

x

2

+

(

x

+

1

)

2

=

5

2

x

2

+

x

2

+

2

x

+

1

=

25

2

x

2

+

2

x

−

24

=

0

x

2

+

x

−

12

=

0

(

x

+

4

)

(

x

−

3

)

=

0

Since:  

x

>

0

→

x

=

3

∴

The faster boat travels at  

(

3

+

1

)

=

4

miles/hr; The slower boat travels at 3 miles/hr

Step-by-step explanation:

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.