Question

a bird leaves its nest and travels 20 miles per hour downwind for xx hours. on the return trip, the bird travels 4 miles per hour slower and has 6 miles left after xx hours.a. what is the distance of the entire trip? b. how long does the entire trip take?

Answer 1

The correct answers are:

A) 60 miles; and B) 3.375 hours.

Explanation:

We will use the equation d = rt for this.

For the first leg of the trip, the bird travels 20 miles per hour for x hours.  This gives us the equation

d = 20x

For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour.  He also travels 6 miles less than the return distance, for x hours:

d-6 = 16x

To isolate d, we will add 6 to each side:

d-6+6 = 16x+6

d = 16x+6

We will set the two equations equal to one another, since they both equal d:

20x = 16x+6

Subtract 16x from each side:

20x-16x = 16x+6-16x

4x = 6

Divide both sides by 4:

4x/4 = 6/4

x = 1.5

He travels for 1.5 hours both times.

The first time, 1.5 hours at 20 miles per hour is:

d = 1.5(20) = 30 miles

The original trip is 30 miles.  This makes the entire trip 30(2) = 60 miles.

On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:

24 = 16x

Divide both sides by 16:

24/16 = 16x/16

1.5 = x

If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:

24/1.5 = 30/x

Cross multiplying,

24*x = 1.5(30)

24x = 45

24x/24 = 45/24

x = 1.875

This gives him a total time of 1.5+1.875 = 3.375 hours.

Answer 2

(a) The total distance of the trip is 60 miles

(b) The total time of the motion for the entire trip is 3.375 hours

The given parameters include;

• the speed of the bird in the forward trip = 20 m/h

• time of motion = x

• the speed of the bird in the backward trip in x hours = (20 - 4)m/h = 16 mi/h

• distance remaining to complete the backward trip = 6 miles

The time to complete each trip is calculated as;

$distance = \ speed \times time$

$forward \ distance = backward \ distance\\\\20x = 16x + 6\\\\20x-16x = 6\\\\4x = 6\\\\x = \frac{6}{4} \\\\x = 1.5 \ hr$

The total time of the motion for the entire trip is calculated as follows;

Time = time for forward + time for backward

$time = 1.5 \ hr_{forward} \ \ +\ \ 1.5 \ hr_{\ backward } \ + \ \ \frac{6 \ mi}{16 \ mi/hr} _{\ backward}\\\\time = 2(1.5)hr + 0.375\ hr\\\\time = 3.375 \ hr$

The time for the entire trip is 3.375 hours

The total distance of the trip is calculated as follows;

$total \ distance = forward \ distance + backward \ distance\\\\total \ distance = 20\times 1.5 \ \ + \ 16\times 1.5 \ \ + \ 6 \ miles\\\\total \ distance = 60 \ miles$

Thus, the total distance of the trip is 60 miles

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