Question

sheela can row a boat at tye rate of 4km per hr in still water she takes 8 hrs in going 12 km upstream and 12 km downstream . find the speed of the stream

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Answer 1

Answer:

+t+ = time in hours to go 12 km upstream

+8+-+t+ = time in hours to go 12 km downstream

Let +s+ = the speed of the stream in km/hr

+4+-+s+ = Sheela's speed going upstream in km/hr

+4+%2B+s+ = Sheela's speed going downstream in km/hr

-------------------

Her equation going upstream:

(1) +12+=+%28+4+-+s+%29%2At+

Her equation for going downstream:

(2) +12+=+%28+4+%2B+s+%29%2A%28+8+-+t+%29+

--------------------------

(2) +12+=+32+%2B+8s+-+4t+-+s%2At+

(2) +4t+%2B+s%2At+=+20+%2B+8s+

(2) +t%2A%28+4+%2B+s+%29+=+20+%2B+8s+%29+

(2) +t+=+4%2A%28+5+%2B+2s+%29+%2F+%28+4+%2B+s+%29+

Substitute (2) into (1)

(1) +12+=+%28+4+-+s+%29%2At+

(1) +12+=+%28+4+-+s+%29%2A4%2A%28+5+%2B+2s+%29+%2F+%28+4+%2B+s+%29+

(1) +3%2A%28+4+%2B+s+%29+=+%28+4+-+s+%29%2A%28+5+%2B+2s+%29+

(1) +12+%2B+3s+=+20+-+5s+%2B+8s+-+2s%5E2+

(1) +2s%5E2+=+20+-+12+

(1) +2s%5E2+=+8+

(1) +s%5E2+=+4+

(1) +s+=+2+

The speed of the stream is 2 km/hr

check answer:

(1) +12+=+%28+4+-+2+%29%2At+

(1) +12+=+2t+

(1) +t+=+6+

and

(2) +12+=+%28+4+%2B+2+%29%2A%28+8+-+t+%29+

(2) +12+=+6%2A%28+8+-+t+%29+

(2) +8+-+t+=+2+

(2) +t+=+8+-+2+

(2) +t+=+6+

Answer 2

$\large\underline\mathrm\red{Given:-}$

• Sheela can raw a boat at 4km/hr in still water she takes 8 hrs in going 12 km upstream and 12 km downstream.

$\large\underline\mathrm\red{To \: find}$

»★Speed of the stream.

$\large\underline\mathrm\red{Solution}$

• Let the stream be x km/hr

• Speed of upstream = (4 - x) km/hr

• Speed of downstream = (4-x)km/hr

★ Time = distance/speed

• Time taken to cover 12 km upstream = 12/4-x

• Time taken to cover 12km downstream = 12/x+4

$\large\underline\mathrm\red{According \: to \: question}$

»★Sheela takes 8 hours to travel 12 km upstream and 12km downstream.

$\large\mathrm{⇢{12}/{4 - x} + {12}/{4 + x} = 4</p><p>}$

$\large\mathrm{⇢12(4+x) + 12(4-x)/12-{x}^{2}=8}$

$\large\mathrm{⇢{48 + 48}/{16-x}^{2}=8}$

$\large\mathrm{⇢{96}/{8}=16-{x}^{2}}$

⇢ $\bf 12 = 16 - {x}^{2}$

⇢ $\bf {x}^{2} = 4$

⇢ $\bf {x} = \sqrt{2}$

⇢ $\bf {x} = {2}$

✰ So,  The speed of the stream x = 2km/hr.