Question

A streamer goes downstream from point A to B in 9hrs .from B to A ,upstream it takes 10h .if the speed is 1km/hr , what will be the speed of the streamer in still water ? also find distance between the point A to B

Answer 1

Answer:

$Speed\ of\ streamer\ in\ still\ water=19\ km/hr\\\\Distance=180\ km$

Step-by-step explanation:

$Let\ speed\ of\ steamer\ in\ still\ water=x\ km/hr\\\\Let\ distance\ between\ A\ and\ B=d\ km$

Downstream:

$Speed of stream=1\ km/hr\\\\Downstream\ speed=speed\ of\ steamer+speed\ of\ stream\\\\Downstream\ speed=x+1\\\\Time\ Taken=9\ hrs\\\\Distance=d\\\\Distance=speed\times time\\\\d=(x+1)\times 9\\\\d=9x+9\ ..................................................eq(1)$

Upstream:

$Speed of stream=1\ km/hr\\\\Upstream\ speed=speed\ of\ steamer-speed\ of\ stream\\\\Downstream\ speed=x-1\\\\Time\ Taken=10\ hrs\\\\Distance=d\\\\Distance=speed\times time\\\\d=(x-1)\times 9\\\\d=10x-10\ ..................................................eq(2)$

$From\ eq(1)\ and\ eq(2)\\\\10x-10=9x+9\\\\10x-9x=10+9\\\\x=19\\\\from\ equation\ 2\\\\d=10x-10\\\\d=10\times 19-10=190-10\\\\d=180$

$Speed\ of\ streamer\ in\ still\ water=19\ km/hr\\\\Distance=180\ km$