## Tuesday, January 19, 2010

### Escalator Races

Two friends were in a hurry to get to a meeting at work and jumped on two parallel escalators going up. One friend was running up the escalator with the speed 1 stair per second and got to the top after 20 steps. Another friend was jumping two stairs per second and got to the top after 16 jumps. During the meeting these friends argued how many stairs long was this escalator: more than 100 or less. What do you think? How many stairs long are this escalator?
(adapted from the book by C. Koval)

Enter your answer on our Family Puzzle Marathon page. Solve three and get a prize!

Kim said...

P1 went 20 stairs and got to the top in 20 seconds. The escalator moved the rest of the stairs.

P2 went 16(2) stairs and got to the top in 16 seconds. The escalator moved the rest of the stairs.

(X-20)/20 = (X-32)/16

16X-20(16) = 20X-32(20)
16X-320 = 20X -640
320=4X
X=80

Kim said...

To be more complete:

if there are 80 stairs,

P1: walks 20 and is moved 60 in 20 seconds
P2: walks 32 and is moved 48 in 16 seconds

in both cases, the stairs move 3/sec, so that's a good check.

Maria said...

Wow: Kim solves correctly, Kim explains beautifully and I am sure she votes! We are having an interesting tight Senate seat race today in Massachusetts.

Kim and Alin are now running side-by-side with 29 puzzles each. Who will cross the 30 puzzle line first?