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

2. let x1 be the distance travelled during this time t by the first biker
    x2 the distance travelled by biker 2 in t
x1=v1*t=10t
x2=v2*t=5t

45 miles apart means x1+x2=45

15t=45
t=3 hours

anonymous · Answer

1. not 100% sure

in both cases the plane travels the same distance
then 5(v+40)=6(v-40)
v=440 miles/hour

anonymous · Answer

2. r*t = d
Solve the following for t:
10 * t + 5 * t = 45
t = 3 hours