Question

A boat with speed 15 km/hr in standing water goes 30 km downstream and returns in a total of 4.5 hours. what is the speed of current?

Answer 1

solution:

[tex]speed of water = 15km/hr distance travelled upstream and downsteam =30km\\ let,speed of stream be x km/hr\\ so,time taken to travel 30km upstream=\frac{30}{15-x}\\ and,time taken to travel 30km downstream = {30}{15+x}\\ time taken to travel 30km upstream and 30km downstram = 4hr30min or 9/2 hr.\\ so, the equation formed will be\\ \frac{30}{15-x}+\frac{30}{15+x}=9/2\\ 30(\frac{1}{15-x}+\frac{1}{15+x})=9/2\\[/tex][tex]\frac{1}{15-x}+\frac{1}{15+x}=\frac{9}{2\times30}=\frac{3}{20}\\ \frac{15+x+15-x}{225}-x^2=\frac{3}{20}\\ \frac{30}{225-x^2}=\frac{3}{20}\\ 225-x^2=\frac{3\times20}{3}\\ 225-x^2=200\\ x^2=225-200\\ x^2=25\\ x=5[/tex]