Dog covers as much ground in 2 leaps as Rabbit covers in 3. Dog is 50 dog leaps behind Rabbit when chase starts.

Question

How many leaps does each make before the Rabbit is caught?

Number of Dog leaps:

Number of Rabbit leaps:

Answer 1

Dorothy, this is a complicated problem, but we can figure it out.

 

First, we have that the ratio of dog to rabbit leaps is 2:3. Since the dog has aleady gone 50 dog leaps...

 

2:3 = 50:r, if r is the number of rabbit leaps.

 

Since 2 x 25 = 50, r = 3 × 25 = 75, so the rabbit has to take 75 leaps to get to where the dog is with his lead.

 

But, the dog will have gone ANOTHER 50 leaps while the rabbit does his 75, so now the rabbit is at 75 and the dog is at 100.

 

Hey, we're getting closer! Another 50 dog leaps and another 75 rabbit leaps, and they are both at 150.

 

Since the dog had a head start, we subtract away the 50 leaps. The dog goes 100 leaps and the rabbit goes 150 leaps before they meet again.

Answer 2

For every leap the dog does, the rabbit covers only 2/3 of the distance.

The rabbit is 50 (dog) leaps ahead.

 

L represents number of dog leaps

 

L = 50 + (2/3)L

(1/3)L = 50             subtract (2/3)L from both side

L = 150                  multiply both sides by 3.

 

Not sure?

 

While the dog is doing 150 leaps the rabbits does 100. That allows the dog to make up the 50 leaps late start.