A bird leaves his nest and travels 20 miles per hour downward for x hours. On the return trip the bird travels 4 miles per hour slower and has six miles left after x hours. What is the distance of the entire trip? How long does the entire trip take
d = 20mi/h * xh = 20x miles.
d = (20-4)mi/h * xh + 6 = 20x
16x + 6 = 20x, X = 1.5 Hours.
d = 20 * 1.5 = 30 Miles from nest.
Dt = 2 * 30 = 60 Miles. = Total distance traveled.
d = V*t = 30, 20*t1 = 30, t1 = 1.5 Hours.
16*t2 = 30, t2 = 1.875 Hours.
t1+t2 = 1.50 + 1.875 = 3.375 Hours.
To find the distance of the entire trip, we need to calculate the distance traveled on the downward trip and the distance traveled on the return trip.
Let's start by finding the distance traveled on the downward trip. We know that the bird travels at a speed of 20 miles per hour for x hours. So the distance traveled on the downward trip is given by distance = speed × time = 20x miles.
Now, let's find the distance traveled on the return trip. We are given that the bird travels 4 miles per hour slower on the return trip. So the speed on the return trip is (20 - 4) = 16 miles per hour. We also know that the bird has six miles left after x hours. This means that the distance traveled on the return trip is the total distance minus the distance left, which is (20x - 6) miles.
To find the entire distance, we need to add the distance of the downward trip and the distance of the return trip. So the total distance is 20x + (20x - 6) = 40x - 6 miles.
To find the time taken for the entire trip, we can divide the total distance by the average speed. The average speed is the total distance divided by the total time. The total distance is 40x - 6 miles, and the total time is x (since the bird spent x hours on both the downward and return trips). Therefore, the average speed is (40x - 6)/x miles per hour.
The time taken for the entire trip is the total distance divided by the average speed: (40x - 6)/(40x - 6)/x = x hours.
So the distance of the entire trip is 40x - 6 miles, and the time taken for the entire trip is x hours.