Question

17. A greyhound pursues a hare and takes 5 leaps for every 6 leaps of the hare, but
3 leaps of the hound are equal to 5 leaps of the hare. Compare the speed of the
hound and the hare,​

Answer 1

Solution :

A greyhound pursues a hare and takes 5 leaps for every 6 leaps of the hare, but 3 leaps of the hound are equal to 5 leaps of the hare.

Let us assume that the distance covered by the hare in one leap is x m .

In 5 leaps ;

The hare covers 5x metres.

But this is covered by the hound in 3 leaps.

So, the hound covers a distance of ( 5/3 ) x metres per leap .

Now ,

The hound can take 5 leaps in the same time interval for which the hare takes 6 leaps.

Distance travelled by the hound in 5 leaps :

> ( 5/3 ) x × 5

> 25/3 x metres .

Distance travelled by the hare in 6 leaps :

> 6x metres.

The ratio of speeds of the hound to that of the hare :

> 25/3 : 6

> 25 : 18 .

This is the required answer .

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Additional Information :

It's quite obvious that the speed of the hound is greater than that of the hare, so the hound will be able to catch the hare after sometime .

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Answer 2

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ A grey hound pursues a hare and takes 5 leaps for every 6 leaps of the hare, but 3 leaps of the hound are equal to 5 leaps of the hare.

${\large{\bold{\rm{\underline{To\; find}}}}}$

★ The speed of the hound and the hare

${\large{\bold{\rm{\underline{Solution}}}}}$

★ The speed of the hound and the hare = 25:18

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ As it's given that a grey hound pursues a hare and takes 5 leaps for every 6 leaps of the hare, but 3 leaps of the hound are equal to 5 leaps of the hare.

~ So firstly let us assume a metres as the distance covered by the hare in one leap.

Ok now let's talk about 5 leaps,.! As it's cleared that the hare cover the distance of 5a metres.

~ But 3 leaps of the hound are equal to 5 leaps of the hare.

Henceforth, (5/3)a meters is the distance that is covered by the hound.

~ Now according to the question,

Hound pursues a hare and takes 5 leaps for every 6 leaps of the hare..! (Same interval)

~ Now the distance travelled by the hound in it's 5 leaps..!

• (5/3)a × 5

• 25/3a metres

~ Now the distance travelled by the hare in it's 6 leaps..!

• 6a metres

~ Now let us compare the speed of the hound and the hare. Let us calculate them in the form of ratio..!

• 25/3a = 6a

• 25/3 = 6

• 25:18