1.

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.

Answer» let the speed of boat `= x`km/hr
speed of stream `=y `km/hr
speed of boat downstream =`x+y `km/hr
speed of boat upstream `x-y`km/hr
time taken `t_1= 30/(x-y)`hrs
`t_2 = 44/(x+y)` hrs
`t_1 + t_2 = 10`hrs
`30/(x-y) + 44/(x+y) = 10` eqn(1)
`t_3 = 40/(x-y)`hrs
`t_4 = 55/(x+y)`
`= 40/(x-y) + 55/(x+y) = 13` eqn(2)
let `1/(x-y) = A & 1/(x+y) = B`
`30A + 44B = 10`
`40A + 55B = 13`
`B= (13-40A)/55`
`30A + 44((13-40A)/55) = 10`
`15A + (22*((13-40A)/55))= 5`
`75A + 2(13-40A) = 5`
`75A + 26 - 80A = 25`
`A=1/5`
`B = (13-40*1/5)/55 = (13-8)/55 = 1/11`
`1/(x-y) = 1/5`
`1/(x+y) = 1/11`
`x-y= 5`
`x= 5+y`
& `x+y =11`
`5+y +y =11`
`5+2y=11`
`y = 6/2=3`km/hr
`x = 3+5 = 8`km/hr
answer


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