Question

The speed of a Garden-Snail is 50 metres per hour and that of the Cheetah is 120 kilometers per hour. Find the ratio of the speeds.

Answer 1

Hint: In this question first we had to make the unit of speed of snail and cheetah similar. i.e. we had to convert the speed of the snail from m/hr to m/s and the speed of the cheetah from km/hr to m/s. After that we can easily simplify their ratio by dividing their speeds.

Complete step-by-step answer:
As we know that the ratio between any two things is just a comparison between them which we can find by dividing both of them but the result should be in fraction not in decimal.
As we know that if we divide two things then their units should always be the same.
Now as given in the question that,
Speed of garden-snail = 50m/hr
And as we know that,
1 hour = 60 minutes
1 minute = 60 seconds
So, for converting hours in seconds, speed must be divided by 60\[ \times \]60
So, the speed of Garden- snail must be equal to \[\dfrac{{50}}{{60 \times 60}}\] m/s
On, solving the above equation the speed of the snail will get converted to m/s and hence speed of the snail becomes \[\dfrac{1}{{72}}\] m/s
Similarly, we had to convert the speed of cheetah from km/s to m/s.
And as we know that,
1 km = 1000m
So, to change the unit of speed from km/hr to m/s we had to multiply by 1000 (to change from km to m) and divide by \[60 \times 60\] (to change from hours to seconds)
So, the speed of cheetah will become \[120 \times \dfrac{{1000}}{{60 \times 60}}\] m/s = \[\dfrac{{100}}{3}\] m/s
Now as we can see that now units of speed of Cheetah and Snail are the same.
So, now to find the ratio of speed of snail and cheetah we had to divide both of their speeds. i.e.
Ratio = \[\dfrac{{{\text{Speed of Snail}}}}{{{\text{Speed of Cheetah}}}}\] = \[\dfrac{{\dfrac{1}{{72}}}}{{\dfrac{{100}}{3}}} = \dfrac{3}{{7200}} = \dfrac{1}{{2400}}\]
Hence, the ratio of speed of Ground-Snail and Cheetah will be equal to \[\dfrac{1}{{2400}}\]


Note:- For solving any such problem one should remember that the units of both the speeds must be similar. We can also convert both speeds in km/hr but the answer will remain the same because the ratio is unitless. And to convert the speed of an object from km/hr to m/s we can just multiply the speed in km/hr by \[\dfrac{5}{{18}}\] to the speed in m/s. And to change the unit from m/s to km/hr we had to multiply the speed in m/s by \[\dfrac{{18}}{5}\] to get the required speed in km/hr.