Mile and Time Downwind Distance

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? X = speed of plane in still air (x+40) = speed of plane downwind (x-40) =speed of plane against the wind distance = speed *travel time downwind distance = headwind distance
5(x+40) = 6(x-40)
5x+200=6x-240

6x-5x=240+200
x=440 mph
So, The speed of the plane in still air is 440 mph if I am not mistaken.
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?
D=RT
45=(10+5)T
45=15T
T=45/15
T=3 hours.
3. Jesse rents a moving van for $75 and must pay $2 per mile. The following week, Alex rents the same van, is charged $80 for the rental and $1. 50 per mile. If they each paid the same amount and drove the same number of miles, how far did they each travel? 5+2m=80+1. 5m subtract 75 from both sides subtract 1. 5m from both sides .5m=5 multiply both sides by 2 m=10 miles.
4. During the 4th of July weekend, 32 vehicles became trapped on the Sunshine Skyway Bridge while it was being repaved. A recent city ordinance decreed that only cars with 4 wheels and trucks with six wheels could be on the bridge at any given time. If there were 148 tires that needed to be replaced due to damage, how many cars and trucks were involved in the incident? Okay. There were 32 cars, we have x + y = 32 ars have 4 wheels so 4x, trucks have 6 wheels so 6x the total number of wheels adds up to 148, so
4x +6y = 14: x+y=32
4x + 6y = 148 -4x – 4y = -128
4x + 6y = 148.
5. For this question, you will need a parent/guardian or a friend. Have this individual grab a handful of coins making sure there are only two types of coins in the group (i. e. , nickels and dimes, quarters and pennies, pennies and dimes, etc). Your parent/guardian or friend should tell you the type of coins they’ve chosen, how many coins they have, and the dollar amount of the group.
From this information, you will set up two sets of equations and determine how many of each coin they have in their hand. Please send your instructor the name of the individual who helped you with this question, your two equations, and the work you did to solve the system. She has 11 coins worth 83 cents. P and Q will the number of pennies and quarters,
P + Q = 11
P + 25Q = 83
P + 25Q – P + Q = 24 Q = 83 – 11 = 72.
So, 24 Q = 72
Q = 3.
Q = 3 can be put into the equation to solve for P. If we use the first equation, we get P + 3 = 11 P = 8, so three quarters and eight pennies.