SOLUTION: A brother and sister walk home from school at the same constant speed. One day fifteen minutes after they left the school the sister realized she had forgotten her lunch bag. The b

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Question 927531: A brother and sister walk home from school at the same constant speed. One day fifteen minutes after they left the school the sister realized she had forgotten her lunch bag. The brother ran back to the school, picked up the lunch bag, and ran after his sister. After the brother caught up with the sister, the siblings continued at their regular speed, but arrived home 6 minutes later than usual. How many times faster than their normal walking speed did the brother run?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the distance from school to home +1+ unit of distance
Let +t+ minutes = their normal time from
school to home
--------------------------
In a +15+ minutes period, they walked a distance
+%28+1%2Ft%29%2A15+=+15%2Ft+
The brother ran twice this distance to
get lunch bag and bring it back to his sister
( who must have been standing still )
He ran a distance of:
+2%2A%28+15%2Ft+%29+=+30%2Ft+
He ran this in +6+ min ( the extra time )
+%28%28+30%2Ft+%29%29+%2F+6+=+5%2Ft+
----------------------
Their normal rate was +1%2Ft+, so he
ran 5 times their normal walking rate