Question

On the second leg of a certain journey, a person traveled at an average speed $50$ percent greater than the average speed at which the person traveled the first leg of the journey, and for an amount of time $50$ percent greater than the amount of time spent on the first leg of the journey. Calculate, the person's average speed for the entire journey was what percent greater than the person's average speed on the first leg of the journey.

• A. $22.5\%$
• B. $25\%$
• C. $30\%$
• D. $50\%$
• E. $100\%$

Answer 1

The correct option is C $30\%$

Speed of first leg be $s_1$

Speed of second leg be $s_2$

Time of first leg be $t_1$

Time of second leg be $t_2$

Average speed is $\Rightarrow \frac{s_1\times t_1+s_2\times t_2}{t_1+t_2}=\frac{totaldistance}{totaltime}$

$s_2=1.5s_1$

$t_2=1.5t_1$$\Rightarrow s_{avg}=\frac{s_1\times t_1+1.5s_1\times 1.5t_1}{t_1+1.5t_1}=\frac{s_1\times t_1(1+2.25)}{2.5t_1}=1.3s_1$

$\frac{s_{avg}-s_1}{s_1}\times 100=30$

$s_{avg}$ is $30$% greater than $s_1$