2010 AMC 10A Problem 13

Problem 13 of 25IntermediateAlgebra Arithmetic

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?

Show solution

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.

Tagged: distance rate and time · linear equation