1. A plane travels from Orlando to Denver and back again. On the five-hour trip from Orlando to Denver, the plane has a tailwind of 40 miles per hour. On the return trip from Denver to Orlando, the plane faces a headwind of 40 miles per hour. This trip takes six hours. What is the speed of the airplane in still air? (2 points)
2.Two bicycles depart from Miami Beach going in opposite directions. The first bicycle is traveling at
10 miles per hour. The second bicycle travels at 5 miles per hour. How long does it take until the bikes are 45 miles apart? (2 points)

Question

1. A plane travels from Orlando to Denver and back again. On the five-hour trip from Orlando to Denver, the plane has a tailwind of 40 miles per hour.  On the return trip from Denver to Orlando, the plane faces a headwind of 40 miles per hour. This trip takes six hours. What is the speed of the airplane in still air?  (2 points)
2.Two bicycles depart from Miami Beach going in opposite directions. The first bicycle is traveling at 
10 miles per hour.  The second bicycle travels at 5 miles per hour. How long does it take until the bikes are 45 miles apart?  (2 points)

anonymous · Answer

1. Call the velocity of the plane $v$ and the velocity of the wind $v_w$.  On the trip out, $v_w$ is +40 because it is pushing the plane, making it go faster.
$$distance = rate \times time \
d = (v + v_w) \times 5 = (v + 40) \times 5 = 5v + 200 \Rightarrow d - 5v = 200 $$
Now on the trip back, $v_w$ is -40, because it is slowing the plane.
$$d = (v - 40) \times 6 = 6v - 200 \Rightarrow d - 6v = -200$$
$$d - 5v = 200 \
d - 6v = -200 \Rightarrow v = 400 mph$$

whpalmer4 · Answer

For problem 2, the bikes move in opposite directions, for a net separation speed of 10+5 miles per hour.  After 1 hour, they are 15 miles apart.  How many hours to get 45 miles apart?

anonymous · Answer

$$45 \textrm{ miles} \times \frac{1 \textrm{ hour}}{15 \textrm{ miles}} = 3 \textrm{ hours}$$