Question : A certain distance is covered by a cyclist at a certain speed. If a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is:
Option 1: $1:4$
Option 2: $4:1$
Option 3: $1:2$
Option 4: $2:1$
Correct Answer: $1:4$
Solution :
Given: A certain distance is covered by a cyclist at a certain speed. If a jogger covers half the distance in double the time.
We know the formula, $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$
Let the cyclist travel at $x$ km/h and the distance to be covered takes $y$ hours.
So, the cyclist covered $xy$ km.
Jogger's distance travelled is $\frac{xy}{2}$ km.
The time is $2y$ hours.
The ratio of the speed of the jogger to that of the cyclist is $\frac{xy}{2\times 2y}:x$ or $1:4$
Hence, the correct answer is $1:4$
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