A boat takes total 03 hrs. to cover a distance of 12 km in upstream and comes back 18 km in downstream. While the boat takes 6.5 hrs. to cover a distance of 36 km in upstream and comes back 24 km in downstream. Find speed of the current.
Answer & explanation
Correct answer: option 1
\(\frac{12}{x - y}\) + \(\frac{18}{x + y}\) = 3 ---(i)
\(\frac{36}{x - y}\) + \(\frac{24}{x + y}\) = 6.5 ---(ii)
(i) x 3 - (ii) x 1
\(\frac{30}{x + y}\) = 2.5
x + y = 12,
Put in equation (ii)
\(\frac{36}{x - y}\) + \(\frac{24}{12}\) = 6.5
\(\frac{36}{x - y}\) + 2 = 6.5
\(\frac{36}{x - y}\) = 4.5
\(\frac{36}{4.5}\) = x - y
x - y = 8
Now add & subtract x + y & x - y
x = 10, y = 2