### Need of Speed For Average Speed

A man drives

**1 mile**to the top of a hill at**15 mph**. How fast must he drive**1 mile**down the other side to average**30 mph**for the 2-mile trip?**Here is calculation of that speed needed!**Something to tease your brain!

Showing posts with the label trip

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A man drives 1 mile to the top of a hill at 15 mph. That means he took, 1/15 hours i.e

To achieve average speed of

Let

30 = 2/(1/15 + 1/x)

(1/15 + 1/x) = 2 / 30 = 1/15

1/x = 0

To conclude, it's impossible to achieve average speed of 30mph in trip.

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- Crossing
**one mile**of desert requires using**1 gallon**of water. - Sara can only carry
**6**gallons of water at a time. - Sara can drop a water
**cache**(of any amount of water from the supply she is carrying at that moment) at any of the nine stops along the route, and then pick up any part of the cache on a later trip.

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1. First Sara collects

2.She collect 6 gallons more water at the start of 4th trip from source & drops 5 gallons at milepost 1. Now, she doesn't need to return back to source and

3.In next 2 rounds, she moves

4.Now only

3.Next, using 2 gallons (out of 6 which is maximum she can carry) she moves from

4. Again, on arriving back at milepost 2, she has left with

milepost 4.

5. She uses the remaining

To conclude, Sara has to leave Oasis

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Professor **Fukano** plans to **circumnavigate** the world in his new airplane.
But the plane's fuel tank doesn't hold enough for the trip—in fact, it
holds only enough for *half* the trip. But with the help of **two
identical** support planes (which can refuel him in mid-air) piloted by
his assistants** Fugari** and** Orokana**, the professor thinks he can make it
in one trip. But since all three planes have the same problem of **limited
fuel**, how can they work together to achieve the professor's **goal**
without anyone running out of fuel?

**1.** The professor's plane must make a **single continuous trip** around the world without landing or turning around.

**2.** Each plane can travel exactly **1 degree of longitude in 1 minute**
for every kiloliter of fuel. Each can hold a maximum of 180 kiloliters
of fuel.

**3.** Any plane can **refuel **any of the others in mid-air by meeting at the same point and instantly transferring any amount of fuel.

**4.** **Fugari** and** Orokana's** planes can turn around instantaneously without burning fuel.

**5.** Only **one airport **is available for any of the planes to land, take off, or refuel.

**6.** All three planes must **survive **the experiment, and none may run of fuel in mid-air.

**'This' is how mission is completed!**

** **

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Let's assume that the only airport mentioned is located at the

Recollect all the data given.

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2. Each plane can travel exactly

3. Any plane can refuel any of the others in mid-air by meeting at the same point and instantly transferring any amount of fuel.

4.

5. Only

6. All three planes must

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As per (2), since each plane travel

Let's suppose that, all three planes takes off from airport exactly at 12:00 PM towards the

We will break this 6 hours journey into 8 parts where each plane travels 45 degree of longitude east or west using 45 kiloliters of fuel.

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At this point, each of them will use

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And this is how, exactly at

But is this the most efficient way to make trip around the Earth? Certainly not!

If plane was built with fuel tank of 360 + then the mission wouldn't have required any assistance. Just because of limited fuel tank, 45 + 45 + 90 + 90 + 90 + 90 + 45 + 45 = 270 Kiloliters of fuel burnt to assist Fukano's plane.