A horse thief riding at 8mph has a 32-mile head start. The posse in pursuit is riding at 10 mph. In how many hours would the thief get caught?

Question

Think about the equations representing each situation

Answer 1

distance = speed*time

 

distance/speed = time

 

The posse is traveling 10 mph - 8 mph = 2 mph faster than the thief.  At 2 mph, it will take the posse (32 miles)/(2 mph) = 16 hours to close the gap and catch the thief.

 

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Another way to do it.  Let y = distance traveled and t = time.  For the thief traveling at 8 mph with a 32 mile head start:

 

y = 8t + 32

 

For the posse traveling at 10 mph:

 

y = 10t

 

The posse catches the thief when they have traveled the same distance:

 

10t = 8t+32

 

2t = 32

 

t = 16 hours