Math word problem

Question

A mouse runs past a cat. then 2 and 1/4 seconds later the cat chases the mouse. The mouse runs 2 meters per second and the cat runs 5. if both animals run in a straight line how long will it take the cat to catch the mouse?

Answer 1

Distance = rate x time

 

They both travel the same distance. 

Note that 2 and 1/4 = 2.25

 

 rate for cat x time for cat = rate for mouse x time for mouse

 

         5        x      t             =   2                 x      (t+ 2.25)     <-- mouse travels 2.25 seconds longer than the cat

 

          5t  = 2(t+2.25)

  

         5t = 2t + 4.5

 

        3t = 4.5

 

        t = 1.5 seconds

 

 cat travels 5 m/sec x 1.5 sec = 7.5 meters

 

 mouse travels 2m/sec x (1.5 +2.25) sec = 2 m/sec * 3.75 sec = 7.5 meters.

 

The cat will catch the mouse in 1.5 seconds.

 

      

 

 

 

 

 

 

 

 

 

 

Answer 2

distance = rate*time ...  d= rt

 

We will assume the cat starts off at 5 m/sec

without a lag from the get go since there is

no other information given

 

Let t = time since the mouse passed the cat:

 

Mouse:  d = 2(t)

Cat:      d = 5(t-2.25)   since the cat started running

                                   2 1/4 secs after the mouse

 

Set the two equal to each other and solve for t

 

2t = 5(t-2.25)

2t = 5t - 11.25

3t = 11.25

t = 3.75 seconds or 3 3/4 seconds

 

This is the time the mouse ran since passing

the cat. The cat ran 2.25 seconds less time so

the cat catches the mouse in 3.75-2.25 = 1.5 seconds