Hari starts rowing in a river from a point A to a point B against the flow. As soon as he reaches point B, he immediately starts rowing back to point in the same path. If he takes 5 hours to reach "B" from "A" and 4 hours to reach "A" from "B, then determine the ratio of velocity with which Han can run stl water to velocity of river.
Answers
Answer:
The ratio of velocity with which Hari can run still water to the velocity of the river is Vh /Vr =9
Explanation:
D = distance between A and B.
Vh = velocity of Hari in still water.
Vr = velocity of the river.
Vab = relative velocity of Hari in moving from A to B.
Tab = time in moving from A to B. (given 5 hrs)
Vba = relative velocity in moving from B to A.
Tba = time in moving from B to A. (given 4 hrs)
Now, according to the question we have to find Vh / Vr.
When Hari is moving in ab direction then the river is flowing in opposite direction. So, Vab = Vh - Vr
Similarly, when Hari is moving in ba direction the river is flowing in the same direction. So, Vba = Vh + Vr
Now, Vba /Vab = (D / Tba) / (D / Tab)
=> (Vh + Vr) /(Vh - Vr) = Tab / Tba
=> (Vh + Vr) /(Vh - Vr) = 5/4
Now, using component dividend rule we get:
[(Vh + Vr) + (Vh - Vr)] / [(Vh + Vr) - (Vh - Vr)] = 5+4 /5-4
=> Vh /Vr =9
Therefore, the ratio of velocity with which Hari can run still water to the velocity of the river is Vh /Vr =9:1