Question

Can some one please help me? I've already tryed to figure it out on my own..but its no use!

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?

Could you show me step by step so I understand it!? Thank you <3

Answer 1

[(x + 40) mph](5 hours) = [(x - 40) mph](6 hours)

5x + 200 = 6x - 240

x = 440 mph

Answer 2

The two sides can be set equal to each other because the distance is the same and the units are "miles".

Answer 3

"x + 40" is the combined speed on this first leg of the trip, and "x - 40" is the combined speed on the trip back.

Answer 4

The equation is in "miles" because "hours" times "mph" gives "miles".

Answer 5

ahhh. I think I kind of get it.

Answer 6

Good luck to you in all of your studies and thx for the recognition! @magenxoxo

Let's not stop at a fuzzy understanding. Please ask some questions.

Answer 7

I will try doing the next word problem on my own and run it by u to see if its correct?! :)

Answer 8

The first key to understanding this is that if the plane is pushing itself the same each way, that is "x" mph and with a 40 mph tailwind, it goes x + 40 mph and into the wind it goes x - 40 mph

Answer 9

The second key to understanding this is that rate times time = distance and that is the same both ways. So we get an equation in distance.

Answer 10

yes.. I understand that part :) so we use the distance formula.. d=rt

Answer 11

So, the distances are the same, and that is expressed by the rate of "x + 40" times the time of 5 hours, going there. Coming back we have the rate of "x - 40" times the time of 6 hours. And then we just solve for "x".

Answer 12

As a by-product, though the problem doesn't ask for it. we also know the distance, and that is 2400 miles each way because:

(440 + 40)(5) = 2400

Answer 13

Just as

(440 - 40)(6) = 2400

on the way back.

Answer 14

So, the plane, relative to the ground (not the relative to the air), goes 480 mph going there and 400 mph coming back.

Answer 15

So, that's about all I can add to the understanding of that problem unless you want to ask questions. Or we can go on to another problem.

Answer 16

ok! thank youuu :) i'm actually working on another problem now.. I wanted to try and see if i could do it. but if i need help i'll post it here :)

Answer 17

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?

Answer 18

@blondie16

Answer 19

sorry i dont remember how to do this lol! hmmm let me see @abb0t @hartnn @Hero

Answer 20

haha. its all goooood :)

Answer 21

wouldn't it be 50? bc 10x5=50.... ur talkin about the seccond question i posted? correct?

Answer 22

wouldn't the equation be (10mph)t + (5mph)t???

Answer 23

OOOOOH

Answer 24

idk.. I'm confused

Answer 25

uhm.. 3 hours? haha.... that seems wrongg

Answer 26

2 hours and 25 min?

Answer 27

ahh. yay :) I was right!

Answer 28

Thank youuu!!!

Answer 29

aha.. yeah.. ur right.