(A) Initial distance between the dog and the cat $= 25$ dog leaps.In one minute, the dog makes $5$ leaps.In one minute, the cat makes $6$ leaps. Since

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(A) Initial distance between the dog and the cat $= 25$ dog leaps.In one minute, the dog makes $5$ leaps.In one minute, the cat makes $6$ leaps. Since $1$ dog leap $= 2$ cat leaps, $6$ cat leaps $= 3$ dog leaps.Therefore, the relative speed of the dog with respect to the cat $= 5 - 3 = 2$ dog leaps per minute.Time taken to catch the cat $= \frac{\text{Initial distance}}{\text{Relative speed}} = \frac{25}{2} = 12.5$ minutes.

Competitive Quantitative Aptitude Time and Distances Time and Distances

Easy

$A$ dog finds a cat at $25$ leaps away. The cat sees the dog coming towards it and starts running with the dog in hot pursuit. In every minute, the dog makes $5$ leaps and the cat makes $6$ leaps, and one leap of the dog is equal to $2$ leaps of the cat. Find the time in which the dog will catch the cat (in minutes).

A
$12.5$
B
$13$
C
$11.5$
D
$10.5$

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Time and Distances

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Time and Distances

$A$ man on tour travels the first $160 \, km$ at $64 \, km/hr$ and the next $160 \, km$ at $80 \, km/hr$. What is the average speed for the first $320 \, km$ of the tour (in $km/hr$)?

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$A$ train,after travelling $50 \, km$,meets with an accident and then proceeds at $\frac{3}{4}$ of its former speed and arrives at its destination $35 \, minutes$ late. Had the accident occurred $72 \, km$ further,it would have reached the destination only $15 \, minutes$ late. The normal speed of the train (in $km/hr$) is:

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$A$ boy goes to the school with the speed of $3 \, km/h$ and returns with the speed of $2 \, km/h$. If he takes $5 \, hours$ in all,then the distance (in $km$) between the village and the school is:

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In covering a distance of $30 \, km$,Abhay takes $2 \, hours$ more than Sameer. If Abhay doubles his speed,then he would take $1 \, hour$ less than Sameer. Abhay's speed is (in $km/h$):

Difficult

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Two places $P$ and $Q$ are $162 \, km$ apart. $A$ train leaves $P$ for $Q$ and simultaneously another train leaves $Q$ for $P$. They meet at the end of $6 \, hours$. If the former train travels $8 \, km/h$ faster than the other,then the speed of the train from $Q$ is (in $km/h$):

Medium

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$A$ man on tour travels the first $160 \, km$ at $64 \, km/hr$ and the next $160 \, km$ at $80 \, km/hr$. What is the average speed for the first $320 \, km$ of the tour (in $km/hr$)?

$A$ boy goes to the school with the speed of $3 \, km/h$ and returns with the speed of $2 \, km/h$. If he takes $5 \, hours$ in all,then the distance (in $km$) between the village and the school is:

In covering a distance of $30 \, km$,Abhay takes $2 \, hours$ more than Sameer. If Abhay doubles his speed,then he would take $1 \, hour$ less than Sameer. Abhay's speed is (in $km/h$):

Two places $P$ and $Q$ are $162 \, km$ apart. $A$ train leaves $P$ for $Q$ and simultaneously another train leaves $Q$ for $P$. They meet at the end of $6 \, hours$. If the former train travels $8 \, km/h$ faster than the other,then the speed of the train from $Q$ is (in $km/h$):

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