SOLUTION: Twenty minutes after Melissa’s older sister left home for band practice, Melissa saw that she had forgotten her sheet music, and ran after her. If Melissa runs three times as fas

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Twenty minutes after Melissa’s older sister left home for band practice, Melissa saw that she had forgotten her sheet music, and ran after her. If Melissa runs three times as fas      Log On


   

Question 733965: Twenty minutes after Melissa’s older sister left home for
band practice, Melissa saw that she had forgotten her sheet
music, and ran after her. If Melissa runs three times as fast
as her older sister, how long will it take to reach her?
There is a similar question already posted, but I do not understand the solution. The posted questions is:
Ten minutes after Sasha’s little brother left home for karate
class, Sasha saw that he had forgotten his karate uniform,
and she ran after him. If Sasha runs twice as fast as her little
brother, how long will it take her to reach him?
Can you help me to understand the posted solution? I need to be able to completly understand this problem so I can explain it to others.
THANKS!!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = older sister's speed in mi/hr
+3s+ = Melissa's speed in mi/hr
-----------------------
+20+ min = +1%2F3+ hr
older sister's head start is +s%2A%281%2F3%29+ mi
Let +d+ = distance Melissa has to travel to catch sister
Let +t+ = time to catch her
--------------
Sister's equation:
+d+-+%281%2F3%29%2As+=+s%2At+
Melissa's equation:
+d+=+3s%2At+
------------
+s%2At+%2B+%281%2F3%29%2As+=+3s%2At+
+2s%2At+=+s%2F3+
+t+=+1%2F6+
+%28+1%2F6%29%2A60+=+10+
She catches her in 10 minutes
--------------------------
(2)
+10+ min = +1%2F6+ hr
Let +s+ = little brother's speed in mi/hr
+2s+ = Sasha's speed in mi/hr
-----------------------------
Little brother's head start is +%281%2F6%29%2As+
Let +d+ = distance in mi Sasha has to travel to catch him
Let +t+ = time in hrs to catch him
----------------
Little brother's equation:
+d+-+%281%2F6%29%2As+=+s%2At+
Sasha's equation:
+d+=+2s%2At+
-----------
+s%2At+%2B+%281%2F6%29%2As+=+2s%2At+
+s%2At+=+%281%2F6%29%2As+
+t+=+1%2F6+
+%281%2F6%29%2A60+=+10+
She catches him in 10 minutes
---------------------------
Note that I put in familiar units, but any
units for distance could be used