CPhill

Nice,  tertre  !!!

She is stationary  between  3 PM and 3:30 PM  = 1/2 hr

She is also stationary between 4 PM and 5 PM  = 1 hr

She is also  stationary between 6:30 PM  and 7:30 PM  = 1 hr

Total time  for  the journey  =   6 hrs  [ 8 PM  -  2PM]

So  she is stationary  for  [ 1/2 + 1 + 1/2 ]  =  2 hrs

And she travels   [ 6 hrs  -  2 hrs  ]  =  4 hrs

5 minutes  =  1/12 hr

So

20 km / hr  x   1 / 12 hr   =    [ cancel   hr  ]

20/ 12  km  =

5 /3  km

Yeah, EP....I finally realized that my first answer was correct....

[ Thanks for your reinforcement  ...LOL!! ]

Good.....!!!

Since triangle ABC  is similar to triangle PAQ

Then angle BAC  = angle APQ

But angle BAC  = 70

So angle APQ  = 70

And angle QPC  is supplemental to angle APQ

So angle QPC  = 110

And triangle ABQ  is simialr to triangle QCP

So  angle ABQ = angle QCP  

But angle ABQ  = angle ABC = angle QCP = angle ACB

So...triangle ABC  isosceles  with angles ABC, ACB  being equal

So...their measures  =  [ 180  - m angle BAC ] / 2  =   [180  - 70] / 2  = 110 / 2  = 55

And since m angle ACB  = m angle QCP...then m angle QCP  = 55

So...in triangle QPC......m angle PQC  = [ 180  - m angle QPC - m angle QCP ] =

180  - 110  - 55  = 180 - 165  =   15°  =  m angle PQC

Fiona's answer is correct

See the diagram :

Since  in triangle XBY...angle XBY  = 60

And since  BX  and BY  are tangents to the incircle  drawn from B....then  BX  = BY

And the angles opposite these sides are also equal  = [ 180 - angle XBY ] / 2  =

[ 180 - 60 ] / 2  = 120 / 2  = 60

So angle BYX  = angle BXY  = 60

But angle  BYX  is supplemental to angle AYX  =  180 - 60  = 120 (degrees)

Mmmmm...I  see what you mean, guest....but....if " at the same time" is true...then my original answer is correct

We don't have to consider any permutations because all we are worried about  is  choosing any 5 numbers at one time from a set of 6

Since  C(6,5)   = 6      and only one of these sets is correct

So    ..  1/6   

What do you think???

We have the following equation :

[ 36B  +   6B  +  A }  + [ 4*36  +  6  +  B  ] + [ 36A  + 6 + 5 ] =  [ 216A  + 36 + 30 + 2  ]

[ 42B + A ]   + [ 150 + B ] + [ 36A + 11 ] = 216A + 68

43B + 37A   + 161  = 216A + 68

43B + 93  = 179A

This equation is true when B  = 2  and A  = 1

And the absolute value  of their difference is  l A  - B  l  = l 1  - 2  l  =  l -1  l  =  1

Thanks, fiora  !!!

BTW....good to see you  !!!