A bird leaves its nest and travels 15 miles per hour downwind for x hours. On the return trip, the bird travels 3 miles per hour slower and has 2 miles left after x hours. a. What is the distance of the entire trip?

miles

b. How long does the entire trip take?

_hours
_minutes and
_seconds

A)

10 miles.

B)

0 hours, 40 minutes, and 0 seconds.  

Step-by-step explanation:

Remember that distance is given by the formula:

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:

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:

We can solve this using substitution. Since we already know that d is 15x. Substitute:

Solve for x. Subtract 12x from both sides:

Add 2 to both sides:

Divide both sides by 3:

Therefore, the bird traveled for a total of 2/3 hours or 40 minutes.

And the distance the bird traveled is:

Substitute 2/3 for x to get:

And we're done!