Math Puzzles

[Tricky]

1. <LI>The repeating decimal 0.65141414… can be represented by the fraction c/d, where c and d are positive integers with no common factors greater than one. Find the sum of c and d.
   <LI> The number 95 is listed in both sequence Blue and sequence Red. Find the next number that would also be in both sequence Blue and Red.
   <UL><LI>Blue: 19, 95, 171, 247, 323, . . .
   <LI>Red: 20, 45, 70, 95, 120, . . .

<LI>Mr. Newton drives to and from work over the same route each day. On Friday, he drives at an average rate of 52 mph and is one minute late to work. On Monday, he drives at an average rate of 60 mph and is one minute early to work. If he left home at the same time each day, what is the distance Mr. Newton travels from home (one way) to work?
<LI>A given semicircle has a diameter of 8 inches (segment CD). Chord AB is half the length and parallel to diameter CD. Find the distance from the midpoint of chord AB to the midpoint of diameter CD.[/list]

[pi-eater]

1. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">16349</span hide>
2. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1995</span hide>
3. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">13 mi</span hide>
4. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">4*sqrt(3)</span hide>

[Tricky]

Pi-Eater,

Thanks for playing. I'm, showing that you have Q1, Q2 and Q3 correct. I've got a different solution for Q4.

<img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>

[johnhutchison]

For Q4 I get

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">2sqrt(3) or sqrt(12)</span hide>

[pi-eater]

Absolutely correct. I was working off a radius of 8 instead of diameter of 8. That's what happens when you don't write it down on paper.