Question 1042905
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A steamer goes downstream from one point to another in 9 hours. It covers the same distance upstream in 10 hours. 
If the speed of the stream be 1 km/hr , find the speed of the steamer in still water and the distance between the ports .
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Let D be the distance between the ports (in kilometers), and
let u be the streamer speed in still water.

Then you have these two equations


{{{D/9}}} = u + 1,   (1)    ( speed equation for moving downstream )

{{{D/10}}} = u - 1,  (2)    ( speed equation for moving upstream )

Distract equation (2) from (1) (both sides). You will get

{{{D/9 - D/10}}} = 2  --->  {{{(10D)/90 - (9D)/90}}} = 2  --->  {{{D/90}}} = 2  --->  D = 2*90 = 180.

Thus we found the distance. It is 180 kilometers.

Now from (1),

{{{180/9}}} = u + 1  ---> 20 = u + 1  --->  u = 20-1 = 19.

The treamer speed in still water is 19 {{{km/h}}}.
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