[SPLIT] Distance, rate, time: A helicopter flies north at...

[ultrasonicsite]

Ok let me try doing the question now.

A helicopter leaves Central Airport and flies north at 180 mi/h. Twenty minutes later a plane leaves the airport and follows the helicopter at 330 mi/h. How long does it take the plane to overtake the helicopter?

Gather information:

-The helicopter's speed is 180 mi/h.
-The plane's speed is 330 mi/h.
-The plane leaves 20 minutes after the helicopter does.

ok:

Helicopter = 180 mi/h
Plane = 330 mi/h
Let x = time


-------------------------------------
----------Rate*Time=Distance--
-------------------------------------
Heli | 180mi/h | x | 180x
-------------------------------------
Plane | 330mi/h | x+20 | 330(20+x)
-------------------------------------

Ok, so emm...

Let's see. I'm trying to find out how long it takes for the plane to overtake the helicopter.

I'm trying to figure out time, so:

Time = Distance/Rate no?

x = 180x/180 ?

Erm, no that won't work. :?

I'm so oblivious to something I bet is right in front of my eyes O.O

 

[galactus]

The second chopper will overtake the first when their distances are the same.

The first chopper will travel \(\displaystyle \L\\180t\).

The second: \(\displaystyle \L\\330\underbrace{(t-1/3)}_{\text{1/3 hour=20 min}}\).




Set them equal and solve for t.

 

[ultrasonicsite]

The second chopper will overtake the first when their distances are the same.

The first chopper will travel \(\displaystyle \L\\180t\).

The second: \(\displaystyle \L\\330\underbrace{(t-1/3)}_{\text{1/3 hour=20 min}}\).




Set them equal and solve for t.

Why is it a subtraction instead of an addition if the time when the plane leaves (second chopper) is 20 minutes later?

 

[galactus]

Because he is travelling for 20 minutes less.

If it were positive, you'd get a negative result.

 

[ultrasonicsite]

Ah I see. So I did it kind of "upside down".