A mouse is 20 m away from its burrow and can run at 3m per second. A cat spots the mouse and starts running towards it at 6m per second. (a) How long will it take the mouse to reach its burrow ? (b) If the cat is x meters away from the mouse as shown in the figure , write an expression which tells how long it will take the cat to reach the burrow . (c) If the cat pounces upon the mouse when it is about to enter its burrow, find the value of x. (d) Interpret your result.
Answers
Answer:
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Step-by-step explanation:
Distance between mouse and burrow=20 m
Speed of mouse=3 m per sec]
Distance between cat and burrow=(20+x) m
Speed of cat=6 m per sec
Now,
a) Time=Distance/speed of mouse=20/3=6.67 sec
b) Time=Distance/speed of cat⇒t=20+x/6 (here t is time)
c) If cat pounces upon the mouse when it is about to enter the burrow. It means cat also need 6.67 sec to reach the burrow.
So, put t=6.67 or 20/3 sec into result of part (b), we get
t=20+x/6
⇒20/3=20+x/6
⇒3(20+x)=20×6
⇒60+3x=120
⇒3x=120−60
⇒3x=60
⇒x=20
So, the distance between mouse and cat is 20 m.
d) Interpretation of results are done in each part already.Regards.
(a) time=20/3m
(b) time=20+x/6
(c) 20=3 × 20+x/6
6×20=3(20+x)
120=3(20+x)
120/3=20+x
40=20+x
40-20=x
20m=x