A motor boat goes down the stream 30 kilometer and again returned to the starting point in a total time and4hours and thirty minut

1 thought on “A motor boat goes down the stream 30 kilometer and again returned to the starting point in a total time and4hours and thirty minut”

1. Answer: Speed of motor boat in still water is 15 km/h.
   

   
   

   Step-by-step explanation:Total time taken by the motorboat = 4 hrs 30 minutes = 4 ½ hr = (9/2) hrs
   

   
   

   The distance travelled by boat during downstream = 30 km
   

   
   

   The speed of the stream = 5 km/hr
   

   
   

   Let the speed of the boat in still water be “x” km/hr.
   

   
   

   So,
   

   
   

   The speed of the boat downstream = (x + 5) km/hr
   

   
   

   The speed of the boat upstream = (x – 5) km/hr
   

   
   

   and,
   

   
   

   Time taken to travel downstream = 30/(x+5)
   

   
   

   Time taken taken to travel upstream = 30/(x-5)
   

   
   

   Therefore, according to the question, we can write the eq. as,
   

   
   

   [30/(x+5)] + [30/(x-5)] = 9/2
   

   
   

   ⇒ 30 [(x-5+x+5)/{(x-5)(x+5)}] = 9/2
   

   
   

   ⇒ 30 [(2x) / (x² – 25)] = 9/2
   

   
   

   ⇒ 10 [(2x) / (x² – 25)] = 3/2
   

   
   

   ⇒ 40x = 3x² – 75
   

   
   

   ⇒ 3x² – 40x – 75 = 0
   

   
   

   ⇒ 3x² – 45x + 5x – 75 = 0
   

   
   

   ⇒ 3x(x-15) + 5(x-15) = 0
   

   
   

   ⇒ (x-15)(3x+5) = 0
   

   
   

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