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'Don't Be Late' printed from https://nrich.maths.org/
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 |
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.