IMC 2009 Q19
19. Driving to Birmingham airport, Mary cruised at 55 miles per hour for the first two hours and then flew along at 70 miles per hour for the remainder of the journey. Her average speed for the entire journey was 60 miles per hour. How long did Mary's journey to Birmingham Airport take?
- A 6 hours
- B \(4\frac{1}{2}\) hours
- C 4 hours
- D \(3\frac{1}{2}\) hours
- E 3 hours
Intermediate Mathematical Challenge 2009, Question 19. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 3 hours
Let the time for which Mary drove at 70 mph be \(t\) hours. Then the total distance covered was (55 × 2 + 70 × \(t\)) miles. Also, as her average speed over (2 + \(t\)) hours was 60 mph, the total distance travelled was 60(2 + \(t\)) miles.
Therefore 110 + 70\(t\) = 120 + 60\(t\), that is 10\(t\) = 10, that is \(t\) = 1.
So, in total, Mary's journey took 3 hours.
Solution © UK Mathematics Trust, from the IMC 2009 solutions.