Question 17892
let the speed of the boat be x = 20 mph
let the speed of the current be y mph
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Then speed up stream = x-y = (20-y) mph
Distance up=48 miles
therefore Time[1] = 48/(20-y)
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Speed downstream = x+y = (20+y)mph
Distance=48miles
Time[2]=48/(20+y)
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Total time=5 hours
total time=48(20+y)+48/(20-y)
{{{ (48/(20+y))+(48/(20-y))= 5 }}}
{{{ (48(20-y) + 48(20+y))/((20-y)(20+y)) = 5 }}}
{{{ 48(20-y) + 48(20+y) = 5(20-y)(20+y) }}}
{{{ 2*48*20 = 5(400-y^2) }}}
{{{ (48*40)/5 = 400 - y^2 }}}
{{{ 1920/5 = 400 - y^2 }}}
{{{ 384 = 400 - y^2 }}}
{{{ 384-400 = -y^2 }}}
{{{ -y^2 = -16 }}}
{{{ y^2 = 16 }}}
Hence y=plus or minus 4
Speed of the current in this context cannot be negative,hence
{{{ y = 4 }}}
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Speed of boat=20 mph
Speed of current=4 mph
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Hope this helps,
Prabhat