Anonymous

# Airplane Problem help?

Two planes are flying toward each other. One is flying 240 miles per hour and the other 360 miles per hour. They are 440 miles apart. What will be there distance when they are 4 minutes away from each other? PLease explain I am lost

Relevance

OK... This kind of problem is easiest if you break it down into smaller problems. Also, we need to have everything in the same unit of measurement to make life easier...

Firstly, we need to know how far apart in miles they will be when they are 4 minutes apart. We need to convert the mph figures to mpm (miles per minute) by dividing by the number of minutes in an hour (60). That gives us:

Airplane 1: 240mph/60 = 4mpm

Airplane 2: 360mph/60 = 6mpm

Next, we know the 2 airplanes are moving toward each other. If we add the new figures together, we get the "closing speed" (how fast they are moving toward each other):

4mpm+6mpm = 10mpm

We know that there is 440 miles between them at the start of the problem, and now we know that the airplanes are closing at 10mpm. We can use that to work out how far apart they are in time (we need to know this, because the next part of the problem gives us a seperation in minutes, not miles):

440 miles/10mpm = 44 minutes

So now we know how fast each one is going, and how far apart they are in minutes... Next, we need to know ho long each has traveled in minutes when they have only 4 minutes remaining to go:

44 minutes - 4 minutes = 40 minutes.

So...

Airplane one has flown for 40 minutes at 4mpm

Airplane two has flown for 40 minutes at 6mpm

The distance travelled by each airplane is:

Airplane 1: 40 minutes x 4mpm = 160 miles

Airplane 2: 40 minutes x 6mpm = 240 miles

So, the total distance covered by BOTH airplanes (in the first 40 minutes) is:

160 miles + 240 miles = 400 miles

And we know that there was originaly 440 miles between them, so, the distance between airplane 1 & 2 when they are 4 minutes apart is:

440 miles - 400 miles = 40 miles.

And there you have it!

• They have a closing speed of 600 mph.(240 + 360)

That is a closing distance of 10 miles per minute.(600/60)

4 minutes times 10 = 40 miles apart.

• the slower plane is going 240 mph , or 4 miles per minute.

the faster plane is going 360 mph, or 6 miles per minute

let x=minutes until impact

4x+6x=440

10x=440

x=44

4 minutes before impact would be x-4, or 40

40 mins. x 6 miles per min.+ 40 min. x 4 miles per min.=240+160

=400

so the planes would be 440-400 miles apart, which equals 40 miles.

• 10x 4=40 miles(?)