A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours it can go 40km upstream and 55km downstream. Determine the speed of the stream and that of the boat in still water.

Let the speed of the stream=xkm/hrLet the speed of the boat in still water=ykm/hrUpstream speed=y−xkm/hrDownstream speed=y+xkm/hrtime=distancespeedThe boat goes30km upstream and44km downstream in10hours.Time taken=30y−x+44y+x10=30y−x+44y+x. (1)The boat goes40km upstream and55km downstream in13hours.Time taken=40y−x+55y+x13=40y−x+55y+x.. (2)Let1y−x=uand1y+x=vFrom (1) and (2),30u+44v=10.. (3)40u+55v=13.. (4)Multiply equation (3) with 4 and equation (4) with 3,120u+176v=40... (5)120u+165v=39... (6)subtract equation (6) from (5),176v𕒵65v=40�v=1v=111⇒1y+x=111y+x=11.. (7)From equation (3),30u=10󔼴v30u=10󔼴×11130u=10𕒸=6u=151y−x=15⇒y−x=5.. (8)Adding (7) and (8), we get,2y=16y=8From equation (7),x=11−yx=11𕒼=3