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Two boats met at a point and one of them moves towards West while one towards South. After 2 hours, distance between them is 60 km. Find the speed of the slower boat if the difference in two speeds is 6 kmph.

Updated On: Jan 12, 2026
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Solution and Explanation

Let the speed of the westbound boat be x km/h and the speed of the southbound boat be (x+6) km/h, reflecting a 6 km/h speed difference.
After 2 hours, the westbound boat travels 2x km and the southbound boat travels 2(x+6) km.
The distance between them forms the hypotenuse of a right-angled triangle created by their paths.
Applying the Pythagorean theorem:
The equation is:
\((2x)^2+[2(x+6)]^2=60^2\)
\(4x^2+4(x+6)^2=3600\)
\(4x^2+4(x^2+12x+36)=3600\)
\(x^2+4x^2+48x+144=3600\)
\(8x^2+48x+144=3600\)
\(8x^2+48x−3456=0\)
\(x^2+6x−432=0\)
\((x+24)(x−18)=0\)
The possible solutions are: \(x=−24\) or \(x=18\). 
As speed cannot be negative, the negative solution is rejected.

Consequently, the speed of the westbound boat (the slower boat) is \(x=18\ km/h\).

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