To find the speed of current of the river

Question

A cutter the speed of which is 20km/h in stagnant water sailed 36km against the current and 22km with the current. It has spend 3hours in all trip. What is the speed of the current of the water

 

 

Answer 1

Let x = speed of current, then speed of boat with the current is (20+ x) and the speed against the current is (20-x).  Time = distance/rate so...

 

3 = 22/(20+x) + 36/(20-x)  common denominator is (400-x²)

 

3(400-x²) = 22(20-x) + 36(20+x)  (all divided by 400-x²) which is cancelled out, but remember that x=20 is excluded for the domain.

 

1200-3x² = 440 - 20x + 720 + 36x

 

3x² + 16x - 40 = 0  solve using th\e quadratic formula

 

[-16 +/- sqrt(16² - 4(3)(-40))]/[2(3)] = (-16 +/- sqrt(736))/6 = (-8 +/- 2sqrt(46)) / 3  Since one of the answers is negative (which is impossible) the answer is (-8 + 2sqrt(46)/3 = 1.855