Question

help please with word problems

Answer 1

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)

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? (2 points)

4.)During a 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 to due to damage, how many cars and trucks were involved in the incident? (2 points)

5.)For this question, you will need a Learning Coach 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 Learning Coach 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. (2 points)

Answer 2

For 1), I am thinking about the equation d = rt. "Distance = Rate x Time"
We should model the two trips with this equation:
- d, in both trips, should be the same.
- r, in a tailwind, is the airplane speed added to the windspeed. It makes it go faster. We know windspeeds, so we can just say the rate is 'A + 40", A = airplane speed.
r, in a headwind, is the airplane speed subtracted by windspeed. The windspeed slows the plane down. "A - 40"
- t is given in both cases.

Answer 3

So: d = r t
r=A+40, t=5; First trip: d = (A + 40) * 5
r=A-40, t=6; Secomd trip: d = (A - 40) * 6

Now we just have to solve this system for the value of A.

Answer 4

ok, i think im following you

Answer 5

d = 5A + 200
-(d = 6A - 240) Eliminating d to find A.

0 = -A + 440
A = 440

Answer 6

thankyou so much. :p
i really appreciate it!!!

Answer 7

and you are the only one who helped me

Answer 8

You're welcome. :)

I think 'd = rt' will be useful for the second one as well.
Basically, since the bicycles are moving apart, the rate at which they move apart is the sum of their rates. One is going 5 mph, and one is going 10 mph, so the rate from each other is 10+5 = 15 mph.
d = 15 t

The question just wants us to find t where d = 45. Plug in d, and we can find the t-value. :)

Answer 9

:)
see that helps as well. thankyou again

Answer 10

would # 3be 10?

Answer 11

3) Something I never exactly considered until recently was units and their interaction in equations. Like, if you have a rate like $ per mile, you get the $-value by multiplying by the miles. Like $*mile/mile = $.

To write an equation for the amount they paid in terms of how many miles they went, we would have something like this:
$ = $ + ($ / mile) * miles Total = an initial cost + rate $/mile * miles traveled.
If it doesn't make so much sense, its fine. I just thought that was interesting. :P
-----

C = 75 + 2m
C = 80 + 1.5m

Yep, m=10 appears to be correct. :)

Answer 12

thankyou!!!!

Answer 13

like how you explained number 3. thats pretty cool

Answer 14

Yeah, I think it makes a lot of sense that way. I found it useful in Physics especially, where my teacher likes to place little trick questions with weight/mass in problems.
Weight is measured in N (kg m/s^2), and mass is measured in kg alone. Weight is mass (kg) times gravity's acceleration (m/s^2). So, it makes more sense where the unit comes from.
Trick questions come up whenever you work with mass when you have weight, or the other way around. When you observe units only, however, its hard to miss those little tricks. :P

Answer 15

:P thats interesting way of going about it. ill keep that on my mind for later use
thanks for helpin

Answer 16

Hm, do you need any help with the last two questions?

Answer 17

Now that I think about it, a lot of Algebra word problems probably make more sense described that way:.. lol

vehicles + vehicles = vehicles
cars + trucks = total vehicles
c + t = 32
wheels/vehicle * vehicles + wheels/vehicles * vehicles = wheels
--> 4 wheels/car, 6 wheels/truck
wheels + wheels = total wheels
4c + 6t = 148

Answer 18

I think i got 4 and 5.
4.)148=x(4)+y(6)
x+y=32 y=32-x

148=4x+6(32-x)

x=22
y=10

and 5, im not around ayone else to be able to do this one...

Answer 19

Yep, looks correct to me.

I would if I even had any coins. lol

Answer 20

lol. thats ok. thanks for checkin number 4 or me

Answer 21

You're welcome! Good luck with your Maths. :)