Question

A steamer goes 50km, downstream and 45 km
upstream in 5 hours.In 5 hours 8 hours of minutes it can
50 km, upstream and 45 km. downstream. Find
the speed of the stream and that of the steamer
in still water​

Answer 1

The speed of stream is 5km/hr while the speed of the steamer  in still water​ is 20km/hr.

Step-by-step explanation:

Let the speed of the steamer in still water be x km/hr

Let the speed of the stream be y km/hr

∵ Speed of streamer upstream = (x-y) km/hr

Speed of streamer downstream = (x+y) km/hr

we know that,

Speed = Distance/Time

ATQ,

45/(x-y) + 50/(x+y) = 5 ...(i)

Second condition,

50/(x-y) + 45/(x+y) = 5hrs 8minutes  ...(ii)

Let 1/(x-y) = u & 1/(x+y) = v

∵ (x - y) = 1/u ...(iii)

& (x+y) = 1/v  ...(iv)

45u + 50v = 5 ...(v)

50u + 45v = 5hrs 8minutes or 77/15 hours ...(vi)

Now,

5(9u + 10v) = 5

5(10u + 9v) = 77/15

⇒ 9u + 10 v = 1     ...(i)

⇒ 10u + 9v = 77/75  ...(ii)

Now, Multiplying both sides by 10 in (i) & by 9 in eq. (ii)

⇒ 90u + 100v = 10

   90u + 81v   = 231/25

⇒ 19v = 19/25

v = 1/25

From (i), 9u + 10/25 = 1

9u = 1 - 10/25 = 3/5

u = 3/5 * 1/9 = 1/15

∵ 1/(x-y) = 1/15, 1/(x+y) = 1/25

⇒ x - y = 15, x + y = 25

⇒ x - y = 15

⇒ x + y = 25

2x = 40

x = 40

x = 40/2 = 20 km/hr

Now, 20 - y = 15

y = 5km/hr

Thus, The speed of stream is 20km/hr while the speed of the steamer  in still water​ is 5km/hr.

Learn more: Speed of the stream

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