document.write( "Question 1055579: Three friends anil, bala and chetan, from X to town X to town Y which was 4o km. Anil who had a bike started along with bala while chetan started simultaneously on foot. After some time , anil dropped bala on the way and went back to pick up chetan while bala proceeded to Y on foot. Anil picked up chetan and reached Y at the same time as bala. Anil traveled at 50km/hr. The speed at which bala and chetan walked was 10 km /hr . find the time after which anil turned back ? \n" ); document.write( "

Algebra.Com's Answer #670787 by ikleyn(52813) $\"\"$ $\"About$

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\n" ); document.write( "Three friends Anil, Bala and Chetan, traveled from town X to town Y which was 40 km.
\n" ); document.write( "Anil who had a bike started along with Bala while Chetan started simultaneously on foot.
\n" ); document.write( "After some time, Anil dropped Bala on the way and went back to pick up Chetan while Bala proceeded to Y on foot.
\n" ); document.write( "Anil picked up Chetan and reached Y at the same time as Bala. Anil traveled at 50km/hr.
\n" ); document.write( "The speed at which Bala and Chetan walked was 10 km/hr. Find the time after which Anil turned back? \r
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document.write( "Below is the sketch to solve the problem:\r\n" );
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document.write( "                       d     d\r\n" );
document.write( "     X--------------p-----c-----q--------------Y\r\n" );
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document.write( "You see the points X and Y here. The distance between X and Y is 40 kilometers.\r\n" );
document.write( "The point q is the point where Anil dropped Bala on the way and went back to pick up Chetan.\r\n" );
document.write( "The point p is the point where Anil picked up Chetan.\r\n" );
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document.write( "So, the Anil's   way is  Xq, then qp,  then pY.\r\n" );
document.write( "    the Bala's   way is  Xq  biking    with Anil, then qY walking.\r\n" );
document.write( "    the Chetan's way is  Xp  walking,  then  pY   biking with Anil.\r\n" );
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document.write( "The point \"c\" is the central point at the half of the distance between X and Y.\r\n" );
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document.write( "From the symmetry, it is clear that the distance Xp is equal to qY.\r\n" );
document.write( "     The ratio for it is the fact from the condition that all three travelers came to Y simultaneously.\r\n" );
document.write( "It means that pc = qc, and all we need to do is to find the length pc or qc.\r\n" );
document.write( "I marked this distance as \"d\" in the sketch:  d = pc = qc.\r\n" );
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document.write( "Anil on his bike covered the distance of  Xq + 2d + 2d + qY = 40 + 4d.\r\n" );
document.write( "He spent  hours for the entire journey.\r\n" );
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document.write( "Bala   spent  hours.\r\n" );
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document.write( "Chetan spent  hours, the same time as Bala.\r\n" );
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document.write( "So, the equation to find the unknown \"d\" is\r\n" );
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document.write( " = .\r\n" );
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document.write( "Actually, the problem is just setup and, therefore, solved.\r\n" );
document.write( "The rest is just arithmetic.\r\n" );
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document.write( "The answer is d = 10 km.\r\n" );
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document.write( "So, Xq =  = 30 kilometers, and Anil covered Xq in  =  of an hour = 3*12 = 36 minutes.\r\n" );
document.write( "It is the time after which Anil turned back.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The problem is solved.\r
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\n" ); document.write( "\n" ); document.write( "This problem is classic Travel and Distance problem.
\n" ); document.write( "I remember it from my childhood time, but I never solved it before.
\n" ); document.write( "It is the first time I solved it.\r
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\n" ); document.write( "\n" ); document.write( "Thanks to the person who posted it, for beautiful challenge.\r
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\n" ); document.write( "\n" ); document.write( "By the way, this complicated logistic provides the minimal time for three travelers, who have only one bike, to reach the final point.\r
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\n" ); document.write( "\n" ); document.write( "In response, you can see the bunch of Travel and Distance problems in this site under the link Travel and Distance problems\r
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\n" ); document.write( "\n" ); document.write( "They are the part of my online textbook \r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "You are welcome!\r
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