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A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. find the speed of the board in

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Let us take the speed of boat in still water as v1 speed of stream is v2 in up stream the total relative speed will be v1-v2 in down stream the total relative speed will be v1+v2 According to condition 1 time taken up stream+ time taken down stream = 8hrs we know distance/speed (12/v1-v2)+(40/v1+v2)=8@ Equation 1 On solving (52v1-28v2)=8((v1*v1)-(v2*v2)) Keep that aside now according to condition two (12/v1-v2)+(40/v1+v2)=(16/v1-v2)+(32/v1+v2)=8 on solving we get v1-3v2=0@ Equation 2 Substitute Equation 2 in 1 to get v2 and then v2 in Equation 2 to get v1 final result will be v1=7.31 Km/hr v2=2.43 Km/hr Note: you may notice v2=0 as one of the answers but if v2=0 there is no up stream and down stream

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Let the speed of boat in still water be x speed of stream be y in up stream the speed of boat will be x - y in down stream the speed of boat will be x + y so given, time taken to go up stream+ time taken to go down stream = 8hrs we know distance/speed