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14 May, 19:05

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

+3
Answers (1)
  1. 14 May, 19:30
    0
    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.
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