Friday, February 17, 2012

Friday Puzzle

For a pre-weekend puzzle I've adapted this algebraic riddle from a Math Mom's puzzle of a couple of months back:

Taylor Swift's traveling bus is coming down Melody Blvd. one day, and one of her fans wants to estimate the length of the vehicle while it is steadily, uniformly moving. He walks alongside the moving bus from back to front (same direction as bus is moving), at a consistent speed, and counts 30 steps. Then, immediately, he turns back and walks alongside the bus in the opposite direction, requiring only 15 steps to reach the back end (at the same speed). If every step he takes is consistently 2 feet, then what is the length of the bus?

I'll put Math Mom's approach to a solution in the comments (I computed it slightly differently, but arriving at same answer).


"Shecky Riemann" said...

ANSWER: 40 ft.

take x as the length of the bus in feet and y as how far the bus moves (in feet) when the fan takes 1 step

then when the boy moves in the same direction as the bus:
x + 30y = 30 X 2 = 60

when the boy moves in the opposite direction:
x = 15 X 2 + 15y = 30 + 15y

substitute 30 + 15y instead of x in the first equation:
30 + 15y + 30y = 60
45y = 30
y = 2/3

x = 30 + 15y = 30 + 10 = 40 feet

whitecorp said...

Taylor Swift eh? Btw I love the little writeup about yourself (null set growing on your head and bones getting a wee bit fractal etc). Peace.