. 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.
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. 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.
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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
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