Question

A motor boat whose speed is 18km/hr in still water takes 1hr more to go 24km upstream than to return downstream to the same spot. What is the speed of the stream?

Answer 1

Solution :

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Given :
         The speed of the motor bike instill water is 18 kmph,
         It takes 1 hour to travel upstream & return to same spot,.

From this information we can say that,

⇒ The speed of motor boat (boat's engine) = 18 kmph ,

⇒ It traveled 24 km upstream & 24km downstream in 1 hour,.

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To Find :

The speed of stream .

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We know that,

time = $\frac{distance}{speed}$

So,

Let the speed of stream be x,

Then,

we can say that,

⇒  $\frac{24}{18 - x} - \frac{24}{18 + x} = 1$ .....(i)      (All the units are in hour km per hour,etc,.)

⇒ $\frac{24(18 + x)-24(18 - x)}{(18 - x)(18 + x)} = 1$

⇒ $\frac{24(18 + x - 18 + x)}{(18 - x)(18 + x)} = 1$

⇒ $\frac{24(2x)}{324 - x^2} = 1$

⇒ $324 - x^2 = 48x$

⇒ -x² - 48x + 324 = 0

⇒ x² + 48x - 324 = 0

⇒ x² - 6x + 54x - 324 = 0

⇒ x (x -6) + 54(x - 6) = 0

⇒ (x + 54)(x - 6) = 0

For the equation to be 0,

Either,

⇒ x + 54 = 0 (or) x - 6 = 0

⇒ x = -54 (or) x = 6

⇒ x = 6 (As speed can't be negative, x ≠ -54)

      ∴ The speed of the stream is 6 kmph

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                             Hope it Helps!!

Answer 2

Let the speed of the stream be x km/hr.

Given: Time taken for going upstream is one hour more than the time taken for going downstream. So, tup=tdown+1 ----------(A)

Distance upstream = Distance downstream = 24 km

Speed of the boat going upstream, vup=18−x

Speed of the boat going downstream, vdown=18+x

Time taken going upstream, tup=Distance upstreamSpeed upstream =2418−x

tup=2418−x -------- (1)

Time taken going downstream, tdown=Distance downstreamSpeed downstream =2418+x

or tdown=2418+x --------- (2)

Using equation (1), (2) and (A):

2418−x=2418+x+1

24(18+x)=24(18−x)+(18+x)(18−x)

24∗18+24x=24∗18−24x+182−x2

x2+48x−182=0

x2+54x−6x−324=0

(x+54)(x−6)=0

x =6 (Rejecting negative value of x)