AMC 10 Weekly Practice Round 2
Complete problem set with solutions and individual problem pages
A car and a truck depart from City toward City at the same time. After reaching City , the car immediately returns to City at a different speed, while the truck stops after reaching City . The graphs shown represent the relationship between the distance (in km) from City and the travel time (in hours) for the truck and the car, respectively. When the car is returning from City to City and meets the truck along the way, what is the distance from City to the meeting point?
- A.
- B.
- C.
- D.
- E.
From the problem, the speed of the car on its return trip to City is
Let the function representing the truck’s distance from City with respect to travel time be
Substituting the point gives:
so
Thus, the truck’s distance function is
Let the function representing the car’s distance from City on its return trip be
Substituting the points and gives:
Solving gives:
Thus, the car’s distance function on its return trip is
Solving the system
gives:
Therefore, when the car is returning from City to City and meets the truck, the meeting point is from City .
