Question

Item 20 A bird leaves its nest and travels 20 miles per hour downwind for x hours. On the return trip, the bird travels 4 miles per hour slower and has 6 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

Answer 1

A) total distance covered = 60miles

B) total time taken = 4hrs 30 mins

Explanation:

Detailed explanation and calculation is shown in the image below

Answer 2

A). 30 miles

B). 3 hours 0 minutes 0 seconds

Explanation:

Let's assume that the distance is y and the time to be x

Speed= distance/time

If the bird traveled at a speed of 20mph,it will be

20 = y/x

Y = 20x______ equation 1

And on the Bird's return it took it flew at a speed 4 miles per hour slower and had 6 miles left to cover after x hours

20 - 4 = (y - 6)/x

16 = (y - 6) /x_____ equation 2

From equation 1 which is y = 20x,substitute into equation 2

16 = (20x - 6)/x

Cross multiply the above and we have

16x = 20x - 6

Collect like terms

20x - 16x = 6

4x = 6

X = 6/4

X = 3/2 or 1½ hours or 1 hour 30 minutes for the trip away from the nest

Substitute in equation 1 and we have

20x = y

20 × 1½ =y

Y = 60/2

Y = 30 miles is the distance from the nest to the birds destination prior to it's return

The entire trip took 3 hours since we have to calculate the "going and coming back" of the bird.

And the distance is 60 miles.