Question

a person can row 8 km upstream and 24 km downstream in 4 hours we can row 12 km downstream and 12 km upstream in 4 hours find the speed of flowing in still water and also the speed of current

Answer 1

Let speed of person in still water be x km/hrLet speed of the current be y km/hr1. Speed upstream: x-y 2. Speed downstream: x=y( because we go against the current) (because we go in the direction of current)D = 8km D= 24kmS = x-y S = x+yT1= D/S = 8 / (x-y) T2 = D/S = 24/ (x+y)T = T1 + T2 = 4 hours8/ (x-y) + 24/ (x+y) = 4 --- 12. Upstream Downstream D = 12km D = 12 km S = x-y S = x+y T1 = D/S =12/ (x-y) T2 = D/S = 12/ (x+y)T = T1 + T2 = 4 hours12/ (x-y) + 12/ (x+y) =4 -------- 2let 1/ ( x+y) be "a" and 1 / (x-y) be "b"Elimination method:-

8b + 24a = 4 (from 1){12a +12b = 4} * 2 --- 24a +24b = 8 ( from 2) Subtracting the equations:----

8b +24a - (24a + 24b) =4 - 8-16b = - 4b = 4/16 = 1/424a = 8b24a = 8 * 1/4 a = 2 / 24a= 1/ x+y = 1/12 therefore, x+y= 12 ----- 3b= 1/ x-y = 1/4 therefore, x-y = 4 ------ 43+4 -- x + y +x - y = 12 +4 2x = 16 x = 16/ 2 = 8 x - y = 4 - y = 4 - x = 4 - 8 = -4 y=4

x= speed in still water = 8km/hry=speed of current = 4km/hr

hope it's help you