Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A hare and a Jackal are running a race. Three leaps of the hare are equal to four leaps of Jackal. For every six leaps of the hare, the jackal takes 5 leaps. Find the ratio of their speeds?

I have tried to solve the question like:

speed of Hare = X/3 Speed of Jackal = X/4

so ratio should be 6x/3:5x/4 or 2x:1.25x or 2:1.25

Now I am not very sure that I am following the right process?

share|cite|improve this question
homework should not be used as a standalone tag; see tag-wiki and meta. – Martin Sleziak Feb 26 '13 at 16:44
Thanks. I will keep that in mind. This is my first post. – Pragati Joshi Feb 26 '13 at 16:46

2 Answers 2

up vote 2 down vote accepted

Let $l_h,l_j$ be the leap lengths of the hare & jackal respectively. Let $r_h, r_j$ be the number of leaps per second (rate).

We have $3 l_h = 4 l_j$, or $\frac{l_h}{l_j} = \frac{4}{3}$.

We also have $r_h = \frac{6}{5} r_j$, or $\frac{r_h}{r_j} = \frac{6}{5}$.

Their speeds are given by the leap rate times the leap length, so $\frac{s_h}{s_j} = \frac{l_h r_h}{l_j r_j}= \frac{l_h}{l_j} \frac{r_h}{r_j} = \frac{4}{3} \frac{6}{5} = \frac{8}{5}$.

share|cite|improve this answer

Essentially, yes, your process was correct.

Let's simplify the problem and say that the length of every leap the hare takes is $\frac{4 \textrm{distance units}}{1 \textrm{leap}}$, and the length of a jackal's leap is $\frac{3 \textrm{distance units}}{1 \textrm{leap}}$. The pace of the hare is $\frac{1 \textrm{leap}}{5 \textrm{time units}}$, while the pace of the jackal is $\frac{1 \textrm{leap}}{6 \textrm{time units}}$. Now we can multiply the rates to get the hare's speed as $\frac{4 \textrm{distance units}}{1 \textrm{leap}} \cdot \frac{1 \textrm{leap}}{5 \textrm{time units}} = \frac{4 \textrm{distance units}}{5 \textrm{time units}}$ and the jackal's speed as $\frac{3 \textrm{distance units}}{1 \textrm{leap}} \cdot \frac{1 \textrm{leap}}{6 \textrm{time units}} = \frac{3 \textrm{distance units}}{6 \textrm{time units}}$. Now it is a simple task to find the ratio of their speeds, that is, the ratio of the hare's speed to the jackal's is $\frac{\frac{4}{5}}{\frac{3}{6}} = \frac{8}{5} = 1.6$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.