Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.6 Junior Find the answer

Angelina drove at an average rate of $80$ kmh and then stopped $20$ minutes for gas. After the stop, she drove at an average rate of $100$ kmh. Altogether she drove $250$ km in a total trip time of $3$ hours including the stop. Which equation could be used to solve for the time $t$ in hours that she drove before her stop?
$\textbf{(A)}\ 80t+100\left(\frac{8}{3}-t\right)=250$ $\textbf{(B)}\ 80t=250$ $\textbf{(C)}\ 100t=250$ $\textbf{(D)}\ 90t=250$ $\textbf{(E)}\ 80\left(\frac{8}{3}-t\right)+100t=250$

Your answer

Multiple choice: answer with the letter of the option you want.

Solution

The answer is $A$ because she drove at $80$ kmh for $t$ hours (the amount of time before the stop), and $100$ kmh for $\frac{8}{3}-t$ because she wasn't driving for $20$ minutes, or $\frac{1}{3}$ hours. Multiplying by $t$ gives the total distance, which is $250$ km. Therefore, the answer is $80t+100\left(\frac{8}{3}-t\right)=250$ $\Rightarrow$ $\boxed{(A)}$

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