A bird left it’s nest and traveled 18 miles per hour for x hours. On the return trip, the bird travels 3 miles per hour slower and has 5 miles left after x hours.

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• distance traveled = 18x miles ,  return = 15x miles , given 18x - 15x = 5 miles

3x = 5 , x = 5/3 hours ANSWER

CHECK 18 X 5/3 = 30 MILES  15 X 5/3 = 25 MILES  30-25 = 5 MILES

Source(s): distance traveled is 18x miles return the distance traveled is (18-3)x = 15x miles given 18x -15x = 5 miles , 3x = 5 x = 5/3 hours ANSWER CHECK 18 x 5/3 = 30 miles, 15 x 5/3 = 25 miles , 30-25 = 5 miles
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• distance = rate * time

Distance is unknown, so I'll call that "d".

We know the rate (18 mi/hr)

The time is unknown, called "x".

d = 18x

The return trip was 3 miles per hour slower, so r = 15.

The time "x" is the same.

The distance was 5 miles shy of the first trip, so that distance is "d - 5".

This equation is:

d - 5 = 15x

We now have a system of two equations and two unknowns.  Substitute and solve for x:

18x - 5 = 15x

3x = 5

x = 5/3 hr or 1 hour and 40 min

Now that we know "x", we can solve for "d":

d = 18x

d = 18(5/3)

d = 30 miles

Though you have no question, based on the statements  you gave, the unknowns are:

30 miles in 1 hour and 40 min.

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• (18-3)x =18X-5

18X-3X=18X-5

15X= 18-5

5=3X;

X= 5/3

x=1-2/3 HRS

18x=300

x= 16.6

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• A bird left it’s nest and traveled 18 miles per hour for x hours.

On the return trip, the bird travels 3 miles per hour slower

and has 5 miles left after x hours.

18 x = 15 x + 5

3x = 5

x = 1 2/3 hours

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• Anonymous
2 months ago

Are you asking for the distance or the time spent flying?  You solve this by realizing that distance is the same going each way.

Distance on the first leg = 18 mile/hr * X

Distance on the return leg - 5 miles = (15 mile/hr) *X

Distance on the return leg = (15 mile/hr) *X + 5 miles (2nd equation re-arranged)

18 mile/hr * X = (15 mile/hr) *X + 5 miles

Solve for X.  Once you know the time, you can also use either equation to solve for the distance.

• Total distance

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• Find x ?

or

Find speed ?

Rule

Distance = speed * time

• Total distance

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• 18 * x = (18 - 3) * x + 5

18x = 15x + 5

3x = 5

x = 5/3

18 * 5/3 = 30

15 * (5/3) = 25

25 + 5 = 30

It works.  The bird flew 1hr40min out at 18 mph and flew back for 1hr40min at 15 mph.

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