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Weekly Problem 31 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

Let the time for which Mary drove at $70$ mph be $t$ hours. Then the total distance covered was$55 \times 2 + 70 \times t$ miles. Also, as her average speed over $2 +t$ hours was $60$ mph, so 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.

This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution