Plane airspeed problem: 2 planes leave in opp. directions...

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KingAce

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hey guys, this is the question i've been having a LOT of trouble with. i know it has something to do with D=RT but im not quite sure how to figure this one out.

Problem: Two planes start from Chicago's Ohare International Airport flying in opposite directions. The second plane starts 45 minutes after the first plane, but its speed is 50 miles per hour faster. Find the airspeed of each plane if 3 hrs after the first plane departs, the planes are 2000 miles apart.

Please help! Thanks so much!!
 
Re: Plane airspeed problem

KingAce said:
hey guys, this is the question i've been having a LOT of trouble with. i know it has something to do with D=RT but im not quite sure how to figure this one out.

Problem: Two planes start from Chicago's Ohare International Airport flying in opposite directions. The second plane starts 45 minutes after the first plane, but its speed is 50 miles per hour faster. Find the airspeed of each plane if 3 hrs after the first plane departs, the planes are 2000 miles apart.
Click to expand...
This certainly does have something to do with the relationship "distance = rate * time"

Let x = rate of the first plane
We're told that it travels for 3 hours, so the distance traveled by the first plane is 3x miles.

The second plane leaves 45 minutes later. 45 minutes is 3/4 hours, so the time traveled by the second plane is 3 - (3/4) hours, or (9/4) hours. We also know that the speed of the second plane is 50 mph more than that of the first plane. So, the speed of the second plane is x + 50 mph. Since distance = rate * time, the distance traveled by the second plane is (9/4)*(x + 50).

The planes are traveling in opposite directions, so....

<-----first plane's distance-----><-----second plane's distance------>
<--------------------------------------2000 miles------------------------------->

3x + (9/4)(x + 50) = 2000

Ok...now, solve for x. Be sure to check your answer to see that it satisfies the conditions of the problem.
 
Re: PLANE AIRSPEED PROBLEM! PLEASE HELP!

hmm okay, so think that the total distance the planes travel, if they travel in the same direction is 2000 miles. That's in 3 hours. However, only one plane (we'll call it plane 1) has been flying for 3 hours, the other (plane 2) has been flying only 2 hours and 15 minutes, or 2.25 hours. Also, plane 2 is flying 50 miles faster than the plane 1. So:

let x = plane 1's distance traveled
let z = plane 2's distance traveled
at time (t) = 3hrs. the total distance traveled is 2000 miles. So,
x + z = 2000 at t = 3

the distance formula, as you know, is d = rt
in plane 1's case, d = x, r = a constant, we'll say s, and t = another constant, we'll say t.
so it's formula is:
x = st

plane 2's case, d = z, r = (s + 50) and t = (t - 0.75) <<< 0.75 hours is equal to 45 minutes
so it's formula is z = (s + 50)*(t - 0.75)

you may notice we can plug the formula's x and z into our other equation: x + z = 2000.

Doing so gives us:

2000 = (s + 50)*(t - 0.75) + (st)

plugging in 3hrs. for t will allow us to solve for s, the speed of plane 1, adding 50 to this value will you give you the speed of plane 2.

Seeing how long I've taken typing this, someone else has probably already answered your question, to a better extent than I am capable of - hope I helped though!

Here's my work/the answer:
(try plugging in different numbers and see how it affects the answer)

http://tinyurl.com/25vfcz
 
Problem: Two planes start from Chicago's Ohare International Airport flying in opposite directions. The second plane starts 45 minutes after the first plane, but its speed is 50 miles per hour faster. Find the airspeed of each plane if 3 hrs after the first plane departs, the planes are 2000 miles apart

.......I<....V + 50...>I<..75V.>I<.........V........>I...Speed
------I------------------I----------I-----------------------I
.......I<---------------2000 miles------------------>I...Distance
.......I<....2.25hr...>I<.75hr.>I........2.25hr.....>I...Time

.75V + 2.25V + 2.25(V + 50) = 2000

Solve for V and V + 50
 
Anyway KingAce, solution is not an integer (slower speed works out to 359.5238.....),
so I suggest you check your post for accuracy...these problems usually have integer answers.
 
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