A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of the dog are equal to 4 leaps of the hare. Find the ratio of their speeds.

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Solution

Let x = velocity of dog
y = velocity of hare

t1 = time taken by dog to take one leap
t2 = time taken by hare to take one leap.
A dog takes 4 leaps for every 5 leaps
So,
4t1 = 5t2
=>t1/t2 = 5/4 ....(1)
3 leaps of the dog are equal to 4 leaps of the hare.
So, equating the distance covered
3xt1 = 4yt2
=>x/y = 4/3t2/t1
=>x/y = 4/34/5 (From 1)
=>x/y = 16/15

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