Q. 33

A motorboat whose

Answer :

Given :- Speed of boat =18km/hr


Distance =24 km


Let x be the speed of stream.


Let t1 and t2 be the time for upstream and downstream.


As we know that,


speed= distance / time


time = distance / speed


For upstream,


Speed = (18 x) km/hr


Distance = 24 km


Time = t1


Therefore,


t1 =


For downstream,


Speed = (18 + x) km/hr


Distance =24 km


Time = t2


Therefore, t2 =


Now according to the question-


t1 = t2 + 1




48x = (18 − x)(18 + x)


48x = 324 + 18x 18x x2


x2 + 48x 324 = 0


x2 + 54x 6x 324 = 0


x(x + 54) 6(x + 54) = 0


(x + 54)(x − 6) = 0


x = 54 or x = 6


Since speed cannot be negative.


x = 54 will be rejected


x = 6


Thus, the speed of stream is 6km/hr.


OR


Let one of the odd positive integer be x


then the other odd positive integer is x + 2


their sum of squares = x2 +(x + 2)2


= x2 + x2 + 4x +4


= 2x2 + 4x + 4


Given that their sum of squares = 290


2x2 + 4x + 4 = 290


2x2 +4x = 290 – 4 = 286


2x2 + 4x – 286 = 0


2(x2 + 2x – 143) = 0


x2 + 2x – 143 = 0


x2 + 13x – 11x – 143 = 0


x(x + 13) – 11(x + 13) = 0


(x – 11)(x + 13) = 0


(x – 11) = 0 , (x + 13) = 0


Therefore , x = 11 or – 13


According to question, x is a positive odd integer.


Hence, We take positive value of x


So, x = 11 and (x + 2) = 11 + 2 = 13.


Therefore , the odd positive integers are 11 and 13.


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