2010 AMC 10A Problem 13

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

Subtract the

20

-minute stop from the total time

After the stop, she drives for

3-\dfrac13-t

hours

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.

Problem 13 in other years