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:

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation: