Question
Download Solution PDFA motor boat whose speed is 15 km / hr in still water goes 30 km downstream and comes back in a total of four hours and 30 minutes . What is the speed of the stream in km / hr ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Speed of the motor boat in still water = 15 km/hr
Distance traveled downstream = 30 km
Total time for downstream and upstream = 4 hours 30 minutes = 4.5 hours
Calculation:
Let the speed of the stream be x km/hr.
Speed downstream = (15 + x) km/hr
Speed upstream = (15 - x) km/hr
Time taken to travel downstream = 30 / (15 + x)
Time taken to travel upstream = 30 / (15 - x)
Total time = 4.5 hours
⇒ 30 / (15 + x) + 30 / (15 - x) = 4.5
⇒ 30(15 - x) + 30(15 + x) = 4.5(152 - x2)
⇒ 450 - 30x + 450 + 30x = 4.5(225 - x2)
⇒ 900 = 4.5(225 - x2)
⇒ 900 = 1012.5 - 4.5x2
⇒ 4.5x2 = 1012.5 - 900
⇒ 4.5x2 = 112.5
⇒ x2 = 112.5 / 4.5
⇒ x2 = 25
⇒ x = 5 km/hr
The speed of the stream is 5 km/hr.
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