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:

answer: what do you mean

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.