Physics Word Problem

Question

A rabbit and a turtle race along a 3 km straight road. The turtle runs at 1m/s and the rabbit runs at 5m/s. The rabbit gives the turtle a 5-minute head start. Who wins the race and by what distance?

Answer 1

Let's assume that the road is a safe D-I-R-T (Distance-Is-Rate-times-Time) road.  Usually, with such problems, two of the variables are related or else they are constant.  In this problem the Distance is the same for the turtle and the rabbit.

 

The problem also wants to know the difference of their distances when the rabbit crosses the finish line (and wins), so we will need to find its race time so we can determine the position of the rabbit (unless, of course, the turtle wins and we have to determine the location of the rabbit).

 

O.K. how long does the rabbit take to run the race?      D=RT   so   T=D/R

          T_R = (3 km)/(5 m/s) + (5 min head start)

          T_R = (3 km) (1000 m / km) / (5 m/s)  + (5 min)(60 sec / min)

          T_R = 600 + 300 s

          T_R = 900 sec         (that's 15 minutes)

 

Now, how long does it take the turtle? to run the race

          T_T = (3 km) ( 1000 m / km) / (1 m/s)

          T_T = 3000 sec      (oh, that's 50 minutes -- it lost)

 

And, where was the turtle when the rabbit won?

    Well, in just 15 min (the rabbit's winning time) on the road, the turtle traveled (remember: D=RT):

         D_T = (1 m/s)(900 s)

         D_T = 900 m

That means the rabbit finished the 3 km (that is, 3000 m) course when the turtle was at meter marker (similar to highway mile markers) 900.  Ouch!  that's winning by 2100 m.

Answer 2

3 km=3000 m

a 5 minute head start is a 5*60=300 second head start

the turtle has traveled 300 m in 300 sec

the turtle needs to run 3000-300=2700 m at 1m/s

the rabbit needs to run 3000 m at 5m/s

the turtle needs 2700 seconds to finish the race

the rabbit needs 3000/5=600 seconds to finish the race

the rabbit wins the race because it needs only 600 seconds to cross the finish line compared to the turtle's 2700 seconds

after 600 seconds have gone by, the turtle has traveled 600 meters

the rabbit has already crossed the finish line and the turtle has traveled only 600 meters

the turtle has 2700-600 meters=2100 m left to travel to the finish line

the rabbit won the race by 2100 meters