Fourteen hours after a convict escapes from prison, a guard begins to pursue him. If the convict travels at eight mph on foot and the guard travels at 64 mph by car, how far from the prison will the convict be caught by the guard?

9514 1404 393

  128 miles

Step-by-step explanation:

The convict has a head start of ...

  distance = speed × time

  distance = (8 mi/h) × (14 h) = 112 mi

That distance is being closed at a rate that is the difference between the speeds, so ...

  64 mi/h -8 mi/h = 56 mi/h

The time it takes the guards to catch the convict will be ...

  time = distance/speed

  time = (112 mi)/(56 mi/h) = 2 h

The guards and prisoner will be at a distance from the prison of ...

  distance = speed × time

  distance = (64 mi/h)(2 h) = 128 mi

The convict will be caught 128 miles from the prison.

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Check

The convict will run an additional (8 mi/h)(2 h) = 16 mi after the guards start pursuit. That, in addition to the 112 miles already run, will total 112+16=128 miles, the same distance the guards travel in that 2 hours.

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