An airplane flying at a speed of about 100 mph was once overtaken and passed by a flock of sandpipers! Suppose that a flock of these birds can fly at 110 miles per hour with a certain wind and at 90 mph against it. If they fly a certain distance with the wind and the same distance against it, how far can they fly in all if the trip takes two hours?
a) If x represents the time that the flock spends flying with the wind, how much time does it spend flying against it.
b) Draw a diagram showing the distance flown with the wind and the distance returning against it.
c) Use the information in your diagram to write and equation.
d)solve the equation for x.
e) How far can the flock fly altogether?
a) Let x represent the time that the flock spends flying with the wind. Since the total trip takes 2 hours, the time spent flying against the wind would be 2 - x.
b) To draw a diagram showing the distance flown with the wind and the distance returning against it, you can use arrows or lines to represent the distances. Since the speed of the airplane is 100 mph, the distance flown with the wind would be 110x, and the distance flown against the wind would be 90(2 - x).
c) Based on the information in the diagram, we can write the equation:
Distance flown with the wind + Distance flown against the wind = Total distance flown
110x + 90(2 - x) = Total distance flown
d) To solve the equation for x, we can simplify it:
110x + 90(2 - x) = Total distance flown
110x + 180 - 90x = Total distance flown
20x + 180 = Total distance flown
Now, we need more information to determine the value of x and the total distance flown.
e) Without the total distance flown or the specific value of x, we cannot calculate the exact distance the flock can fly altogether. However, once we have the value of x, we can substitute it into one of the expressions (110x or 90(2 - x)) to find the distance flown in that direction, and then add the distances together to find the total distance flown.