At 1000 hours an aircraft starts from A to fly to B, a flight which will take 4 hours. At 1042 a second aircraft starts the same journey and will complete the flight in 2 hours 30 minutes. If the distance from A to B is 800 miles, at what time will the aircraft be the same distance from B?

- anonymous

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- amistre64

when the distance between the 2 planes = 0 then they are the same distance from pointB

- amistre64

800/4 is the speed of the 1st aircraft
800/(2.5) is the speed of the second aircraft..

- amistre64

200 mph and 320 mph sound about right...

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- amistre64

does 1042 means 42 minutes after 10?

- anonymous

yeah I got the speeds

- anonymous

thats right 45 mins after 10

- amistre64

ok, so if we convert 45 minutes into a fraction of an hour, we will be able to work with it better.... 3/4 or .75 of an hour....

- anonymous

42 mins*
but thats where I got stuck

- amistre64

ok... 60/42 is a good enough fraction to work with :)

- anonymous

yeah got that

- amistre64

divide each by 3... 20/14....10/7....
15/7 seems good... you agree?

- amistre64

10/7 seems good

- anonymous

yeah 10/7 looks ok

- anonymous

these are the options given:
a 1110 hrs
b 1124 hrs
c 1142 hrs
d 1152 hrs

- amistre64

lets make some equations then...
200x + 10/7 = D
320x = D
does that make sense to you?

- amistre64

I think i missed it... we need to know hoe far the first plane has traveled and add that...not the hours...lol

- amistre64

200(10/7) is the "added" distance, or the advantage that the 1st plane has...

- anonymous

ermm .. Y would it be + 10/7. Dont get how the + comes into it

- anonymous

ok that makes sense

- amistre64

200x + 285.7 = D
320x = D
where D is the equal distance flown .... hows that?

- anonymous

yeah that makes sense

- amistre64

makes better sense, but what doesnt make sense to me yet is that it is less than an hour, but the 1st plane has gone more than 200? gotta see where I missed that at :)

- anonymous

hmm ...

- amistre64

200(60/42) = 190.5 looks alot better, musta got it turned around in me head somewhere :)

- anonymous

I didnt get 190.5

- amistre64

7/10 should be our multiplier... 60 is the whole, 42 is the part; part/whole = percent.... .7

- amistre64

200(.7)= 140... that HAS to be it lol maybe

- anonymous

One way to consider it:
Look at the time when only the first is flying; it is going to 200mph for 42 minutes, so will end up 140miles away from A.
NEXT, look at the motion after they are both moving. If you apply a vector of -200mph to both planes, the one that set off first is effectively stationary, so you only need to consider how long it takes the second plane to 'catch up' the 140 mile head start at (320 - 200)mph = 120mph, which is just time = distance over speed. Add the initial 42 minutes and you're done.

- amistre64

200/60 tells us miles per minute; times 42 equals distance traved in 42 minutes...

- amistre64

200x+140 = 320x
140 = 320x - 200x
140 = 120x
x = 140/120 = 14/12 = 7/6...
1 hour and 6/60 minutes.... if it agrees with Newtons :)

- anonymous

oh that make sense
so it should be 200(42/60) = 140 (I.e the distances travelled by plane A)

- amistre64

Yep....
1042 + 0106 = 1148...

- anonymous

but these are the options:
a 1110 hrs
b 1124 hrs
c 1142 hrs
d 1152 hrs

- amistre64

1 hour and 1/6 of another .... ack!! my math is off today...

- amistre64

1hour and 10 minutes... double check that :)

- amistre64

1042+0110 = 1152....

- anonymous

But yes, I agree. Time = 42 minutes + (140/120) minutes = 42 + (7/6) hours = the same as yours.

- anonymous

Ahh .. thanks you

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