A motor boat goes 30km downstream and returns back to the starting point in a total time of 4
hours and 30 minutes. Find the speed of the boat in still water if the speed of the stream is
5km per hour ?
Answers
The speed of the boat in still water is 15 km/hr.
Step-by-step explanation:
Total time taken by the motorboat = 4 hrs 30 minutes = 4 ½ hr = (9/2) hrs
The distance travelled 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 during downstream = 30/(x+5)
Time taken during 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
⇒ x = 15 or -5/3
Neglecting the negative value
⇒ x = 15 km/hr ← the speed of the boat in still water
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