Question

A rabbit runs in a straight line with a velocity of +1.4 m/s for a period of time, rests for 11 s, and then runs again along the same line at +0.67 m/s for an unknown amount of time. The rabbit travels a total distance of 1224 m, and its average speed is 0.84 m/s.

(a) What is the total time the rabbit spends running at 1.4 m/s?
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(b) How long does it spend running at 0.67 m/s?
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Answer 1

Example:

1. Since you know the average speed and the total distance, you can solve for the total time.

Average speed = total distance / total time

rearranging this should give you 1500s for the total time.


2. You know the rabbit rested for 10 seconds, so subtract that from your total time to get 1490s.


3. Set up variables. Say that X is the number of seconds the rabbit was moving at 1.5 m/s (this will be the answer for part a) and say that Y is the number of seconds the rabbit was moving at 0.60 m/s (this will be the answer for part b).


4. Set up an equation. You know that the total time is 1490s so you can set up an equation for X and Y:

X + Y = 1490


5. Set up a second equation. You know that the total distance is 1200m, so you can set up another equation of X and Y based on the speeds.

1.5*X + 0.6*Y = 1200


6. Solve the two equations:
X = 1490 - Y from equation 1
1.5*(1490 - Y) + 0.6*Y = 1200 substitute into equation 2
0.9*Y = 1035 combine like terms
Y=1035/0.9 = 1150 s solve for Y
X = 1490 - (1150) = 340 s plug Y in to find X