Question

On a race, Anjali ran $\frac{3}{4}$ of the time with a good-luck cabbage, and $\frac{1}{4}$ of the time without it. With the cabbage, her running speed was $6$ miles per hour, and her running speed without the cabbage was $12$ miles per hour. The distance that Anjali ran with the cabbage was what fraction of the total distance that she ran?

• A. $0.6$
• B. $0.8$
• C. $0.9$
• D. $0.4$
• E. $0.5$

Answer 1

The correct option is A $0.6$

Let $T$ be the total time.
As Distance $=$ speed $\times$ Time
So, the distance ran by anjali with the cabbage $=6\times \frac{3}{4}T=\frac{9}{2}T$
The distance ran by anjali without the cabbage $=12\times \frac{1}{4}T=3T$
The desired fraction is the distance ran by anjali with the cabbage over the total distance.
$\Rightarrow$ $\frac{\frac{9}{2}T}{(\frac{9}{2}T+3T)}=\frac{\frac{9}{2}}{\frac{15}{2}}=\frac{9}{15}=\frac{3}{5}$ or $0.6$
Hence, option A is correct.