Question

Ryan cycles from his house to the school which is $6\text{km}$ away in $20\text{mins}$. Sean cycles to the school from his house situated $8\text{km}$ away from the school in $32\text{mins}$. The ratio of the speeds of Ryan and Sean will be

• A. $6:5$
• B. $5:6$
• C. $3:4$
• D. $5:8$

Answer 1

The correct option is A

$6:5$

Step 1: Let's convert the unit of time from minutes to hours -

Since, we know that $\text{1 hour = 60 minutes}$,

Therefore, $\text{20 minutes =}\frac{20}{60}\text{hours}=\frac{1}{3}\text{hr}$

$32\text{minutes}=\frac{32}{60}\text{hours}=\frac{8}{15}\text{h}r$

Step 2: Calculating the speed of cycle -

We know that -

Speed of Ryan's cycle = $\frac{6}{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}=\frac{6\times 3}{1}=18\raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$

Speed of Sean's cycle = $\frac{8}{{\displaystyle \raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$15$}\right.}}=\frac{8\times 15}{8}=15\raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$

Step 3: Calculating the ratio of speeds -

The ratio of the speed of Ryan's and Sean's cycle = $\frac{18}{15}=\frac{3\times 6}{3\times 5}=\frac{6}{5}$

= $6:5$

Hence, the ratio of the speeds of Ryan and Sean is $6:5$.