A motor boat whose speed is 18km/h in still water take 1 hour more to go 24km upstream than to return down stream to the same spot. find the speed of stream

Given:- s1 = The speed of the boat = 18km/h. d = Total distance to be covered = 24km one way [either upstream or downstream]. t1 = time taken to go upstream is 't2+1hour' where t2 is time taken to ride downstream. To find:- s2 = speed of the stream. Answer:- Step 1: t1=d/(s1-s2) hours And t2=d/(s1+s2) hours Step 2: t1= t2+1 Step 3: putting step 1 values in 2 d/(s1-s2) = d/(s1+s2)+1. Step 4: Rearranging terms and simplifying 2*(s2)*d/((s1)^2-(s2)^2) = 1 Step 5: Cross multiplying 2*(s2)*d = (s1)^2-(s2)^2 Step 6: Putting values 48 * (s2) = (18)^2 - (s2)^2. Step 7: Rearranging the terms by bringing them to LHS (s2)^2 + 48(s2) - (18)^2 = 0. Solving this we get, s2= -54 and 6km/h As it is speed we take the absolute value and cannot be negative. Speed of stream is 6km/h. 54km/h should be discarded. If stream velocity is higher than boat velocity you can never go upstream. You shall always be going downstream only. The answer where stream velocity comes as 54km/h is a case where you can travel in one direction only. read less

Let the speed of the stream be x km/hr the speed in still water=18 km/hr speed upstream= (18 - x) km/hr speed down stream= (18 + x) km/hr time taken to go upstream=24/(18 - x) hr time taken to go down stream=24/(18 + x) hr time taken to go upstream - time taken to go down stream = 1hr 24/(18 - x) - 24/(18 + x) = 1 24(18 + x) - 24(18 - x) = (18 - x) (18 + x) x^2 +48x - 324 = 0 x^2 + 54x - 6x - 324 = 0 x (x+54) - 6 (x+54) =0 (x- 6)(x+54) =0 x = 6 km/hr [ x = - 54 is not possible as speed cannot be negative] hence speed of the stream is 6 km/hr. read less

let v ( =18 km/h) be the speed of the boat in still water and c be the speed of the stream then, speed of the boat upstream = v - c speed of the boat downstream = v + c let d = distance covered by the boat ( = 24 km) let T be time taken to travel upstream and t be time taken to travel downstream. Since the boat travels the same distance during both the trips we must have speed = distance/time, therefore distance = speed x time distance traveled upstream = distance traveled downstream, (v-c)(T) = (v+c)(t) ......... (1) Also time taken upstream is 1 hour more than time taken downstream therefore T = 1 + t ............ (2) Substitute (2) in (1) to get (v-c) (1+t) = (v+c) (t) solving for t we get t = ( v - c ) / ( 2 c ) .....(3) We know that the speed downstream is given by v + c = d / t ......... (4) Substitute (3) in (4) v + c = d / [ ( v - c ) / ( 2 c ) ] .......... (5) substitute d = 24 km and v = 18 km/h in (5), to get c = 6 km/h read less