A bird leaves it's 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

Step-by-step explanation:

Distance = Speed * time

If a bird leaves it's nest and travels 15 miles per hour downwind for x hours, the distance covered will be:

D = 15x

x = D/15 1

If on the return trip, the bird travels 3 miles per hour slower and has 2 miles left after x hours

Her speed = 15 - 3 = 12mi/hour

If she has 2 miles left after x hours, new distance will be D-2, using the formula for distance:

D+2 = 12x

x = D-2/12   2

Equate 1 and 2:

D/15 = D-2/12

Cross multiply

12D = 15(D-2)

12D = 15D - 30

12D-15D = -30

-3D = -30

D = 10 miles

The distance for the entire trip will be D + (D-2) = 10 + (10-2)

= 10 + 8

= 18 miles

To get the time x, we will substitute D = 10 into equation1

D = 15x

10 = 15x

x = 10/15

To minutes

x = 10/15 * 60

x = 40 minutes

For the going trip

Time taken = x hours

Return trip = x hours

Total time for the entire trip = x+x = 2x

= 2(40)

= 80 minutes

Hence the total time taken for the entire trio will be 1 hour 20minutes