Answer: The boat 1 moves with a speed of 40mi/h, and boat 2 moves with a speed of 20mi/h.
Step-by-step explanation:
First, we know the relation:
Distance = Speed*Time.
We can define the average rate of the boats as the average speed of the boats.
Now, we know that two boats travel in the same direction, let's define:
S₁ = speed of boat 1.
S₂ = speed of boat 2.
We know that one travels twice as fast as the other, then we can write:
S₁ = 2*S₂
We also know that after 3 hours of travel, they are 60mi apart, then if the slower one travelled a distance D in 3 hours, then:
S₂*3h = D
And the faster one will travel D + 60mi
S₁*3h = (D + 60mi)
Then we have the equations:
S₂*3h = D
S₁*3h = (D + 60mi)
We can replace S₁ by 2*S₂ to get:
S₂*3h = D
(2*S₂)*3h = (D + 60mi)
Now we have isolated D in the above equation, we can just replace it in the second equation to get:
(2*S₂)*3h = (S₂*3h + 60mi)
Now we can solve this for S₂
S₂*6h = S₂*3h + 60mi
S₂*6h - S₂*3h = 60mi
S₂*3h = 60mi
S₂ = 60mi/3h = 20mi/h
The speed of boat 2 is 20mi/h
And we knew that:
S₁ = 2*S₂
then:
S₁ = 2*(20mi/h) = 40mi/h
