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Answer: 5 hours
Balancing the speeds
The average speed is 60 miles per hour.
After 2 hours, Mary is 30 behind an average of 60 mph
Each hour, she makes up 10 miles
She will need to do this for 3 hours
Using algebra
Let the time for which Mary drove at 70 mph be $t$ hours.
Then the total distance covered was $45 \times 2 + 70 \times t$ miles.
As her average speed over $2+t$ hours was $60$ mph, the total distance travelled was $60(2+t)$ miles.
Therefore $90 +70t = 120 + 60 t$, that is $10t = 30$, that is $t=3$.
So in total Mary's journey took $5$ hours.
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Age 11 to 14
ShortChallenge Level 
Answer: 5 hours
Balancing the speeds
The average speed is 60 miles per hour.
| speed | relative to average | |
| first hour | 45 | 60$-$15 |
| second hour | 45 | 60$-$15 |
| third hour | 70 | 60 + 10 |
| etc. | 70 | 60 + 10 |
Each hour, she makes up 10 miles
She will need to do this for 3 hours
Using algebra
Let the time for which Mary drove at 70 mph be $t$ hours.
Then the total distance covered was $45 \times 2 + 70 \times t$ miles.
As her average speed over $2+t$ hours was $60$ mph, the total distance travelled was $60(2+t)$ miles.
Therefore $90 +70t = 120 + 60 t$, that is $10t = 30$, that is $t=3$.
So in total Mary's journey took $5$ hours.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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