Motorist Miffed by Mustard Mishap
In order for the distance to be the same clockwise, Matilda travels from A to B, and from B to D.
Given that the distance is the same, and the distance from B to D is 20 miles, the distance from A to B must be 160 miles.
Town E is 80 miles from Town C. Following the counterclockwise route, Matilda goes from A to E, from E to C, and from C to D. That is 20 + 80 + 80 miles, which is 180 miles. The distance from Town A to Town D is 180 miles.
In order for the distance to be the same clockwise, Matilda travels from A to B, and from B to D. Given that the distance is the same, and the distance from B to D is 20 miles, the distance from A to B must be 160 miles.
Candice [email@example.com] must be able to read Minus' mind because her tasty dish is about as good as he could have imagined.
You know that town D is 80 miles from town C. Town E to town C is the same distance as town D to town C and since town D to town C is 80 miles that means town E to town C is also 80 miles.
We also know that town E to town A is 20 miles. Town D to town B is the same distance as town A to town E and since town E to town A is 20 miles that means town D to town B is also 20 miles.
Town A to B to D is equal to town A to E to C to D which is 180 miles. So therefore A to B to D is also 180 miles.
Therefore the solution is the distance from town A to town B is 160 miles. The distance from town A to town D is 180 miles.
Enjoy, from Candice.
Oritt Levi [firstname.lastname@example.org] impressed Minus with this precisely executed recipe to sucess. Oritt, Minus is crazy about your idea of a leading female shark for his upcoming Disney film. He just wants to know if she'll be as cute as Mickey Mouse's girlfriend.
Well, we know that:
ae = 20
bd = 20
cd = 80
ec = 80
And we need to know ab and ad.
Going counter clockwise, we see that:
ae + ec + cd = ad
20 + 80 + 80 = 180
ad - bd = ab
180 - 20 = 160
So ad = 180 and ab = 160
P.S I reckon Minus the Math Shark would make a beautiful Disney movie. However, there needs to be a princess-shark for him to fall in love with . . . how about Multiply, the beautiful Math Shark-ette?
Taryn Chua of Methodist Ladies' College proves once again that she is a master chef -- well, for fickle sharks anyways. We should also give her credit for a solution she submitted last week. We had mistaken her for a "Member of Tradc Technology." Taryn, did you know that the signature on your e-mail reads: "This EMAIL message was sent to you by one of the members of Tradc. Of course please feel free to check out our homepage at...?" Hence, the mix-up.
(all measurements in miles)
Town A to Town B = X
Town A to Town E = 20
Town B to Town D = same as above. ie. 20
Town D to Town C= 80
Town E to Town C = same as above. ie. 80
So, this means:
Town A to Town C = 100
Town B to Town C = 100
As Matilda says that whatever way she goes (clockwise or counterclockwise), she will travel the same distance, then this means:
First: A to D, via E, C = (A to C) + (C to D) = 180
Then: A to D, via E,C = A to D, via B
180 = 20 + X
160 = X
So, the distance from Town A to Town D is 180 miles, and the distance from Town A to Town B is 160 miles (and mad motorists shouldn't even be ALLOWED near hotdog stands, who knows what disaster might come about?)
We're beginning to think John [email@example.com] is a young mathematical genius. Okay, John, fess-up. Who are you really? The math boy wonder? Einstein's re-incarnation? A pint-sized math professor? We're onto you... ;-)
Minus, it's me again.
If you haven't lost your appetite, you may as well munch through this.
Firstly, with the given information, I stated that distance AE was 20, CD was 80, CE = CD = 80, BD = AE = 20, ABD = AECD equals 180. Then if distance AB was ABD minus 20 distance AB would be 160. Now we know that the distance from A to B is 160 miles.
Secondly, the question asks to calculate the distance from A to D. I wasn't sure if it meant to calculate 'as the crow flies' or by the road. Firstly, I made an attempt at finding the distance from A to D as the crow flies. By drawing a straight line from A to D I calculated that the distance was 145 miles. But by the road I easily calculated that the distance from A to D via E and C was 180.
Alexander Williams [firstname.lastname@example.org] shows us that it's pretty easy to come up with a simple little dish for dessert. Short, sweet, and to the point!
A to E to C to D = 180 Miles; A to B to D is also 180 miles. B to D = 20 miles; Subtract 20 miles from 180 miles; therefore A to B = 160 miles.