Thread: adventitious angle driven problem

Mario drives at the average speed at all times with his old car. He makes it from point A direct to point C in 30 minutes; from point A through point B to point C in 35 minutes; and from point A through point D to point C in 40 minutes. Distance from point B to point C is 10 kilometers, the same distance from point C to point D. By the way angle C is 90 degrees. Points A, B, C and D are 4 corners of a quadrilateral and labeled in a clockwise manner. How fast does Mario drive in km/hour?

I'm assuming you're familiar with Law of Sines/Cosines.
To write a FULL step by step solution here would be almost impossible;
classroom environment required (blackboard, chalk.....).

I'll give you a "how to get started".

Draw an approximate representative diagram (quad ABCD); join AC.

Let AB = b, AC = c, AD = d, average speed = x.

Get b,c,d in terms of x (assuming you're familiar with speed = distance/time):
b = (7x - 120) / 12, c = x / 2, d = (2x - 30) / 3
(notice that x > 120/7)

Now you need to calculate a few angles, like B; using triangle ABC:
B = arccos[(b^2 + 100 - c^2) / (20b)] : the 100 is 10^2 (side BC).

It's sure not an easy problem! Good luck.

thanks for the reply, but i have done that already. Like isolating triangle ABD, and summing up their angles = 180 degrees. But the answer was an error . . . . Why not make a complete step by step solution for this? It will frustrate you. Maybe I was wrong with my steps but, that is it. It made some cracks in my skull, emotionally. Where's Grandad?
But i will rework my busted solution, your suggestion maybe right . . . .thanks though

Didn't get a way to solve directly...yet...maybe there isn't one...

Let AB = b, AC = c, AD = d, average speed = x.
Using iteration (7digit accuracy):
x = 39.1496625, b = 12.8373031, c = 19.5748313, d = 16.0997750

Program method I used:
vary x
b = (7x - 120) / 12, c = x / 2, d = (2x - 30) / 3
get angle A using triangle ABD [this uses the hypotenuse 10sqrt(2)]
get angle B using triangle ABC: B = B - 45
get angle D using triangle ACD: D = D - 45
stop when (A + B + D) * 10^7 = 180 * 10^7

Wilmer, thanks for giving time to this type of problem. Do you mean that this problem can not be solved directly but by ITERATION? Wow! i will try your method, thanks for the help, i hope i can get something . . . .your answer x = 39.1496625 km/h is reasonable enough.

Originally Posted by pacman

> Do you mean that this problem can not be solved directly but by ITERATION?

I said I didn't THINK it can be solved directly!

> your answer x = 39.1496625 km/h is reasonable enough.

That is the PRECISE answer to 7digit accuracy (not just reasonable!)

.

Thanks Wilmer.