A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30km

1.	A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30km upstream and 21 km downstream in 13 / 2 hours. Find the speed of boat in still water and also speed of the stream.Its urgent.....
Answer» Answer: The speed of boat in STILL water is 10 km/hr and the speed of STREAM is 4 km/hr Step-by-step explanation: Let the speed of boat in still water be x Let the speed of stream be y Upstream Speed = x-y Downstream speed = x+y Case 1 ) Distance of upstream = 24 km Time = $\frac{Distance}{Speed}$ Time = $\frac{24}{x-y}$ Distance of down stream = 28 km Time = $\frac{Distance}{Speed}$ Time = $\frac{28}{x+y}$ Since we are given that total time is 6 hours So, $\frac{24}{x-y}+\frac{28}{x+y}=6$ ---A Case 2) Distance of upstream =30 km Time = $\frac{Distance}{Speed}$ Time = $\frac{30}{x-y}$ Distance of down stream = 21 km Time = $\frac{Distance}{Speed}$ Time = $\frac{21}{x+y}$ Since we are given that total time is 13/2 hours So, $\frac{30}{x-y}+\frac{21}{x+y}=\frac{13}{2}$ ---B Solve A and B $\frac{24}{x-y}+\frac{28}{x+y}=6$ $]\frac{30}{x-y}+\frac{21}{x+y}=\frac{13}{2}$ Let $\frac{1}{x-y} = u$ and $\frac{1}{x+y} =v$ So, $24u+28v=6$ ----1 $30u+21v=\frac{13}{2}$ ---2 Multiply 1 with 5 and 2 with 4 $120u+140v=30$ ---5 $120u+84v=26$ ---6 Subtract 6 from 5 $120u+140v-120u-84v=30-26$ $140v-84v=4$ $56v=4$ $v=\frac{4}{56}=\frac{1}{14}$ Substitute the value of v in 5 $120u+140(\frac{1}{14})=30$ $120u+10=30$ $120u=20$ $u=\frac{20}{120} =\frac{1}{6}$ So, $\frac{1}{x-y} = \frac{1}{6}$ and $\frac{1}{x+y} =\frac{1}{14}$ $x-y=6$ --- 7 and $x+y=14$ ---8 Add 7 and 8 $x-y+x+y=6+14$ $2x=20$ $x=10$ Substitute in 8 $10+y=14$ $y=4$ HENCE the speed of boat in still water is 10 km/hr and the speed of stream is 4 km/hr