<PRE><B>Question 157087</B>
Rachel loves to color and she can use both hands at same time. When she uses one of her fat crayons it wears down to nothing after 15 hours. Her skinny crayons wear down to nothing after coloring after 6 hours. One day she starts coloring at 10:30am and was given 2 crayons of same height, one fat and one skinny. She began coloring with both crayons, one in each hand. AT WHAT TIME WILL SKINNY CRAYON BE 1/2 HEIGHT OF FAT CRAYON?
:
Let t = the time (in hrs) for this to happen
:
Choose a convenient height for the crayons, height = 15 cm
:
Find the coloring rate for each crayon.
:
{{{15/15}}} = 1 cm/hr for the fat crayon
and
{{{15/6}}} = 2.5 cm/hr for the skinny crayon
:
the equation:
Skinny crayon = half fat crayon
15 - 2.5t = .5(15 - t)
15 - 2.5t = 7.5 - .5t
15 - 7.5 = +2.5t - .5t
7.5 = 2t
t = {{{7.5/2}}}
t = 3.75 hrs or 3 hr 45 min
:
10:30 am + 3:45 = 2:15 pm</PRE>