Answer:
Let the speed of the stream be x km/hr. Then speed upstream \[=(24-x)km/hr.\] and speed downstream \[=(24+x)km/hr.\] Time taken to cover 32 km upstream \[=\frac{32}{24-x}hrs.\] Time taken to cover 32 km downstream \[=\frac{32}{24+x}hrs.\] \[\therefore \] Time difference \[=\frac{32}{24-x}-\frac{32}{24+x}=1\] \[32[(24+x)-(24-x)]=(24-x)(24+x)\] \[32(24+x-24+x)=576-{{x}^{2}}\] \[64x=576-{{x}^{2}}\] \[{{x}^{2}}+64x-576=0\] \[{{x}^{2}}+72x-8x-576=0\] \[x(x+72)-8(x+72)=0\] \[(x+72)(x-8)=0\] \[x=8\] or \[-72\] \[\therefore x=8\] (As speed can?t be negative) \[\therefore \] Speed of the stream is \[8\,km/h.\]
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