Question

. A boat covers 32km upstream and 36km downstream in 7 hours. Also, it covers 40km

upstream and 48km downstream in 9 hours. Find the speed of the boat in still water and

that of the stream.​

Answer 1

Let the speed of the boat in still water be x km/hr and the speed of the stream but y km/hr. Then,

Speed upstream =(x−y)km/hr

Speed downstream =(x+y) km/hr

Now, Time taken to cover 32km upstream =x−y32 hrs

Time taken to cover 36 km downstream =x+y36 hrs

But, total time of journey is 7 hours.

∴x−y32+x+y36=7 ..(i)

Time taken to cover 40km upstream =x−y40

Time taken to cover 48 km downstream =x+y48

In this case, total time of journey is given to be 9 hours.

∴x−y40+x+y48=9 (ii)

Putting x−y1=u and x+y1=v in equations (i) and (ii), we get

32u+36v=7⇒32u−36v−7=0 ..(iii)

40u+48v=9⇒40u−48v−9=0 ..(iv)

Solving these equations by cross-multiplication, we get

36×−9−48×−7u

Answer 2

Step-by-step explanation:

Let the speed of the boat in still water be x km/hr and the speed of the stream be y km/hr .

Then ,

speed upstream= {x-y} km/hr

speed downstream= { x+y}km/hr

Now , time taken to cover 32 km upstream

= 32/ x-y hrs

Time taken to cover 36km downstream

= 36 / x+y hrs

But , Total time of journey is 7 hour

32 / x-y + 36 / x+y = 7 ...(1)

Time taken to cover 40km upstream

= 40/x-y

Time taken to cover 48 km downstream

= 48/ x+y

In this case , total time of journey is given to be 9 hours

40 / x-y + 48/ x+y = 9 ...(2)

Putting 1 / x-y = u and x+y = v in Equation 1 and 2 , we get

32u + 36v = 7 = 32u - 36v = 7 = 0 ...(3)

40u + 48v = 9 = 40u + 48v= 9 =0...(4)

Solving These equation by cross multiplication,we get

u / 36× -9 -48 × -7 = -v / 32 × -9-40×-7 = 1 / 32× 48 - 40 ×36

= u / -324+ 336 = -v / -228+280 = 1 / 1536 - 1440

= u / 12 = v/ 8 = 1 / 96

= u = 12 / 96 and v = 8 / 96

= u = 1/8 and v= 1/12

Now u = 1 / 8 = 1 / x-y = 1 / 8 = x - y = 8 ...(5)

And v = 1 / 12 = 1 / x+y = 1 / 12 = x+y = 12 ...(6)

solving equations 5 and 6 , we get x = 10 and y = 2

Hence , the speed of the boat in still water = 10km/ hr

And speed of the stream = 2 km / hr

Hope it helps you