Question

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?

• A. $\frac{180-x}{2}$
• B. $\frac{x+60}{4}$
• C. $\frac{300-x}{5}$
• D. $\frac{600}{115-x}$
• E. $\frac{12000}{x+200}$

Answer 1

The correct option is E $\frac{12000}{x+200}$

$V_{av}=\frac{TotalDistance}{TotalTime}$

Let Total Distance be $D$

Now, Let us find Time $T_1,T_2$

$\Rightarrow T_1=\frac{\frac{D\times x}{100}}{40}$

$\Rightarrow T_2=\frac{\frac{D\times (100-x)}{100}}{60}$

Now, using above formula

$V_{av}=\frac{D}{T_1+T_2}$

$V_{av}=\frac{D}{\frac{Dx}{4000}+\frac{D(100-x)}{6000}}$

Solving it, we get

$V_{av}=\frac{12000}{x+200}$