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Question 63394: A treasure is located at a point along a straight road with towns A, B, C and D on it in that order. A map gives the following instructions for locating the treasure: a) start at town A, and go 1/2 of the way to C. b) then go 1/3 of the way to D. c) then go 1/4 of the way to B, and dig for the treasure. If AB= 6 miles, BC= 8 miles, and the treasure is buried midway between A and D, find the distance from C to D. Can this be done?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! A treasure is located at a point along a straight road with towns A, B, C and D on it in that order. A map gives the following instructions for locating the treasure: a) start at town A, and go 1/2 of the way to C. b) then go 1/3 of the way to D. c) then go 1/4 of the way to B, and dig for the treasure. If AB= 6 miles, BC= 8 miles, and the treasure is buried midway between A and D, find the distance from C to D. Can this be done?
..AP=7 MILES........BP=1 MILE...SEE BELOW FOR CALCULATION
A-------------------B--P------------R-----Q---C---------------------------D
AB=6 MILES.............BC=8 MILES..............CD=X MILES SAY
START FROM A...HALF WAY TO C SAY UP TO P...SO AP = (8+6)/2=7 MILES
FROM P THEN 1/3 RD WAY TO D..THAT IS TO Q SAY ...PQ=PD/3 = (AD-AP)/3
=(14+X-7)/3=(7+X)/3
FROM Q GO 1/4 WAY TO B SAY TO R THE TREASURE POSITION ..THAT IS QR = QB/4
= (AQ-AB)/4=[AP+PQ-AB]/4=[{7+(7+X)/3}-6]/4
=(10+X)/12
BUT THE TREASURE IS AT MIDWAY BETWEEN A TO D.......AR = (14+X)/2
AR = AQ-QR=AP+PQ-QR=[7+{(7+X)/3}-(10+X)/12]=[84+28+4X-10-X]/12=(102+3X)/12=(34+X)/3
(14+X)/2 = (34+X)/3
28+2X=34+X
X=6 =CD
CD = 6
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