A bird leaves its nest and travels 18 miles per hour downwind for x hours. One the return trip, the bird travels 3 miles per hour slower and has 5 miles left after x hours. 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:

Let y represent the distance travelled downwind by the bird from its nest.

Time = distance/speed

A bird leaves its nest and travels 18 miles per hour downwind for x hours. Time spent in travelling downwind is

x = y/18

One the return trip, the bird travels 3 miles per hour slower and has 5 miles left after x hours. It means that the speed at which the bird travelled is 18 - 3 = 15 mph. Also, the distance covered in x hours is (y - 5) miles. Therefore,

x = (y - 5)/15

Since the time is the same, then

y/18 = (y - 5)/15

Cross multiplying, it becomes

15y = 18(y - 5)

15y = 18y - 90

18y - 15y = 90

3y = 90

y = 90/3

y = 30

a) The distance of the entire trip is

30 + 30 = 60 miles

b) time taken for the trip from the nest is

x = y/18 = 30/18

Time taken to return is

x = (y - 5)/15 = (30 - 5)/15 = 25/15

Time for the entire trip is

30/18 + 25/15 = 900/270

= 3 90/270 = 3 1/3 hours

= 3 hours + 1/3 × 60 minutes

= 3 hours 20 minutes

The total trip took 3 hours, 20 minutes and 0 seconds.