Answer:
A)
10 miles.
B)
0 hours, 40 minutes, and 0 seconds.
Step-by-step explanation:
Remember that distance is given by the formula:
[tex]d=st[/tex]
Where d is the distance, s is the speed, and t is the time.
We know that the bird leaves its nest and travels 15 miles per hour for x hours. So, let's substitute 15 for s and x for t:
[tex]d=15x[/tex]
On the return trip, the bird travels 3 miles per hour slower and has 2 miles left after x hours.
Since this is the return trip, the distance d remains the same. We know that the bird travels 3 miles per hour slower, so it's speed is 15-3 or 12 miles per hour.
However, after x hours, it still has 2 miles left until reaching the destination. So, we will subtract 2 from d. This gives us the equation:
[tex]d-2=12x[/tex]
We can solve this using substitution. Since we already know that d is 15x. Substitute:
[tex]15x-2=12x[/tex]
Solve for x. Subtract 12x from both sides:
[tex]3x-2=0[/tex]
Add 2 to both sides:
[tex]3x=2[/tex]
Divide both sides by 3:
[tex]x=2/3[/tex]
Therefore, the bird traveled for a total of 2/3 hours or 40 minutes.
And the distance the bird traveled is:
[tex]d=15x[/tex]
Substitute 2/3 for x to get:
[tex]d=15(2/3)=30/3=10\text{ miles}[/tex]
And we're done!
