the difference of the squares of the speed of a boat in still water and the speed of the river is six times the speed of the boat in still water. find the average speed of the boat in covering a round trip. (assume all speeds are in kmph)
Answers
Given :- The difference of the squares of the speed of a boat in still water and the speed of the river is six times the speed of the boat in still water. find the average speed of the boat in covering a round trip. { All speed are in km/h.}
Solution :-
Let us assume that,
- Speed of boat in still water = x km/h .
- Speed of river = y km/h .
A/q,
→ (x² - y²) = 6 * x
→ (x - y)(x + y) = 6x --------- Eqn.(1)
now,
→ Round trip = Upstream speed + Downstream speed .
→ Upstream speed = (x - y) km/h .
→ Downstream speed = (x + y) km/h .
so,
→ Average speed = 2 * Upstream speed * Downstream speed / (Upstream speed + Downstream speed)
→ Average speed = 2(x - y)(x + y) / (x - y + x + y)
→ Average speed = 2(x - y)(x + y) / 2x
→ Average speed = (x - y)(x + y)/x
putting value from Eqn.(1) ,
→ Average speed = 6x/x
→ Average speed = 6 km/h (Ans.)
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