Question

Angelina drove at an average rate of $80$ kph and then stopped $20$ minutes for gas. After the stop, she drove at an average rate of $100$ kph. 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?

$80t + 100\left(\dfrac83 - t\right) = 250$

$80t = 250$

$100t = 250$

$90t = 250$

$80\left(\dfrac83 - t\right) + 100t = 250$

Solution:

Before the stop, Angelina drove $80t$ km.

The stop takes $\frac{1}{3}$ of an hour, so her total driving time is $3-\frac13=\frac83$ hours. After the stop, she drives for $\frac83-t$ hours, covering $100\left(\frac83-t\right)$ km.

The total distance equation is $80t+100\left(\frac83-t\right)=250.$

Thus, A is the correct answer.

2010 AMC 10A Problem 13

Solution:

Problem 13 in Other Years