A motor boat goes down the stream 30 km and again returns to the
starting point in a total time of 4 hours and 30 minutes. If the speed of the
stream is 5 km/hr, then find the speed of the motor boat in still water.
Answers
Speed of motor boat in still water is 15 km/h.
Step-by-step explanation:
The speed of the boat in still water is 15 km/hr.
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
⇒ x = 15 or -5/3
Neglecting the negative value
⇒ x = 15 km/hr ← speed of the boat in still water