A river is running at 2 kmph. A boat goes 40 km upstream from A to B and also returns back from B to A in total 10 hours. The speed of the boat in still water is:
Show answer & explanation
Correct answer: D
Explanation
The Correct answer is Option 4 i.e. 8.47 kmph.
Suppose the speed of the boat in still water is x;
So,
Time to go upstream = 40/(x - 2)
Time to go downstream = 40/(x + 2)
According to the question,
Time upstream + Time downstream = 10 hours
⇒ 40/(x - 2) + 40/(x + 2) = 10
⇒ 40(x + 2) + 40(x - 2) = 10(x2 - 4)
⇒ 40x + 80 + 40x - 80 = 10x2 - 40
⇒ x2 - 8x - 4 = 0
⇒ x = [-(-8) + √((-8)2 - 4(1)(-4))]/(2 × 1)
⇒ x = (8 + √(64 + 16))/2
⇒ x = (8 + √80)/2
⇒ x = ±(8 + 4√5)/2
⇒ x = 4 + 2√5
So, the speed of the boat in still water
= 4 + 2√5 = 8.47 kmph
Therefore,
The speed of the boat in still water is 8.47 kmph.