Math Is Fun Forum

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Helicopter problem

You are a pilot of a medical evacuation helicopter. At 5:30 am, you receive word that a passenger  on a ship fell ill and needs to be airlifted as quickly as possible to the nearest hospital, which is where you and the helicopter are located. The cruise ship is 400 miles away from you, where the nearest hospital is found. The ship is making it's way at 10 mph to your port. Your helicopter only has 6600 pounds of fuel, and it burns 1,200 pounds of fuel every hour when it is airborne. Airlifting a passenger takes 30 minutes. Federal law mandates that pilots most retain an hours worth of fuel at all times. If your helicopter travels at 150 miles per hour, at what time must you leave the ship to get to the ship as quickly as possible?
This was one of my practice HW problems and the answer is apparently not 5:30.AM
Could someone give me a detailed explanation on why this isn't 5:30 AM and what the answer is?
THOUGHT PROCESS;
The helicopter can obviously not travel for more than 5 hours since it must maintain an hours worth of fuel.
Now the heli and boat have a 400 mile distance between eachother.
x = time since 5:30 AM
y = time after 5:30 AM when starting the helicopter
now the helicopter's traveled distance is 150(x-y), and the boat's distance is 10x. Summing these expressions, we get 160x-150y = 400, which is (16/15)x- 40/15.
Getting to the ship as quick as possible is minimizing both x and y, and I got 2.5,0.
So is it 8:00 AM?

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,641

Re: Helicopter problem

hi Mathegocart

Work back from the available fuel.  6600 to start but 1200 must be kept as reserve and half hour = 600 for the transfer so the helicopter has 6600 - 1200 - 600 = 4800 for its journey.  It must go out and back so it can travel to a point at sea 2400 pounds of fuel away from the hospital = 2 hours of flight time.

In 2 hours the ship will cover 20 miles and the helicopter 300 miles so they won't meet.  That's why the helicopter must wait while the ship gets nearer before taking off.

So wait while the ship travels 80 miles, then set off and meet at a point 300 miles from the hospital. 

I'm assuming the two must be stationary during the transfer.  You could shave a bit more off the time if the helicopter can meet the ship, turn around and match its speed while both travel towards the land.  Then once the passenger is aboard the helicopter, it is nearer the hospital so won't take 2 hours to get there.  Can you re-calculate using this interpretation? post back if you want me to try it.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Helicopter problem

Accordingly  the helicoter must start at 11.30 A.M and reach the hospital at 4 P.M. It is not clear what is happening during half an hour of airlifting. If it is moving with its same speed during this period then helicopter has to move 5 miles less and and reaches 2 minutes earlier.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Helicopter problem

hi Mathegocart

Work back from the available fuel.  6600 to start but 1200 must be kept as reserve and half hour = 600 for the transfer so the helicopter has 6600 - 1200 - 600 = 4800 for its journey.  It must go out and back so it can travel to a point at sea 2400 pounds of fuel away from the hospital = 2 hours of flight time.

In 2 hours the ship will cover 20 miles and the helicopter 300 miles so they won't meet.  That's why the helicopter must wait while the ship gets nearer before taking off.

So wait while the ship travels 80 miles, then set off and meet at a point 300 miles from the hospital. 

I'm assuming the two must be stationary during the transfer.  You could shave a bit more off the time if the helicopter can meet the ship, turn around and match its speed while both travel towards the land.  Then once the passenger is aboard the helicopter, it is nearer the hospital so won't take 2 hours to get there.  Can you re-calculate using this interpretation? post back if you want me to try it.

Bob

Thank you, bundy, but I do not clearly get the answer. Would it be 1:30 PM?

Last edited by Mathegocart (2016-07-26 10:06:56)

---

The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Helicopter problem

hi Mathegocart

Work back from the available fuel.  6600 to start but 1200 must be kept as reserve and half hour = 600 for the transfer so the helicopter has 6600 - 1200 - 600 = 4800 for its journey.  It must go out and back so it can travel to a point at sea 2400 pounds of fuel away from the hospital = 2 hours of flight time.

In 2 hours the ship will cover 20 miles and the helicopter 300 miles so they won't meet.  That's why the helicopter must wait while the ship gets nearer before taking off.

So wait while the ship travels 80 miles, then set off and meet at a point 300 miles from the hospital. 

I'm assuming the two must be stationary during the transfer.  You could shave a bit more off the time if the helicopter can meet the ship, turn around and match its speed while both travel towards the land.  Then once the passenger is aboard the helicopter, it is nearer the hospital so won't take 2 hours to get there.  Can you re-calculate using this interpretation? post back if you want me to try it.

Bob

leave the ship to get to the ship as quickly as possible? We do not go back to the ship and then back to the hospital. We just want to know the time to go to the ship.

---

The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,641

Re: Helicopter problem

Limit on fuel means you must wait for the ship to get close enough and then 2 hours flight time, hospital to ship.

So if you wait for the ship to do 80 miles (8 hours) and then the helicopter sets off, 2 hours later they meet at a distance of 300 miles from the hospital and 100 miles from the ship's original position.

If the 'mayday' is a 5.30am then the helicopter will arrive at the ship at  3.30pm on that day.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Helicopter problem

bob bundy is right. Somehow I misinterpreted that the helicopter reaches the ship at 1.30 P.M. but it actually starts for the ship at 1.30 P.M.

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}