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Hey JimC,

RE " 1/(-4) + 1/2 + 1/2 + 1/4 = 1

Any (of the infinite number of integer) values for a & d that cancel each other out would work."

Well explained, it's easy to follow the logic in the daytime.

OK folks, it's Sunday morning so here's an easy one!

An army motorcyclist is escorting a 20 mile line of military vehicles. He drives at constant speed from his starting place at the back to the front of the line, and immediately returns with the same speed to the back of the line. He arrives at the back just as the line has moved 20 miles. How many miles did the motorcycle travel?

Can't be easy John, no answers yet.

Hmmm yes, lazy Sunday! We'll never get to 200 posts if you don't all pull your socks up!

Here's how you do it:

We know that the motorcyclist ends up 20 miles from where he started, so let's call the extra distance he travelled before he turned X. So he covered 20 + X miles from his starting place
at the back to the front of the line and he covered X miles back again.

Let V and v be the velocities of the motorcyclist and of the vehicles respectively.

So the time to go from back to front is:

(20+X)/V = X/v

and the time to go from front to back again is:

X/V = (20-X)/v

By rearranging those equations we get:

(20+X)/X = X/(20-X) = V/v

so:

X^2 = (20 + X)*(20 - X)

X^2 = 400 + (20 * X) - (20 * X) - X^2

X^2 = 200

X = sqrt(200)

Thus the motorcycle has travelled

20 + (2 * sqrt(200)) = 48.284 miles

John from A

Based on the 20 mile distance on his return then I guess that the end of the line must have been 10 miles from the starting point as he reacvhed the front so he must have travelled 30 mile. His return trip took him back to the 20 mile point a distance of 10 miles, therefore, total miles = 40??

JimB

This thread is becoming very machistic. An awful lot more information is required to be able to work it out logically and accurately, for example:

1. Where are the loos siutuated along the route?
2. Where, when and for how long will we stop for morning coffee?
3. Is there a Sainsbury's or Marks and Spencers along the route (will need to pick up a few things for dinner)?
4. If passing a dress shop with a sale on and some fantastic bargains are to be had, how long will the convoy stop?
5. If best friends' house is two miles along a side street, is a detour permitted?
6. Will those nasty helmets which flatten the best of hairdos be mandatory?
7. Will the motorcyle have heated handgrips?
8. Can the convoy go on its own if it's raining?
9. When and where is lunch being served? (Burger King or McDonalds not being options).

You see, you men never, ever give enough important information!!

Nice one Campo!

Cut straight to the important issues. You obviously graduated from the standard "let's enjoy the trip" school of (feminine) logic.

Jimbo

T SHIRTS spotted being worn by POSERS OF THE DAY. This should get the posts well on the way to 200.

I have kleptomania,
But when it gets bad,
I take something for it.

My wife walked out on me because I'm a compulsive gambler. How can I win her back?

Terry

Is it really her back you want?

JimB