A cat travels across gardens at 240 metres an hour and returns on the same route at 160 metres per hour -- what is his average speed?

Remember the basic equation of velocity:


Distance = Velocity \ *\ Time


Here we want to find the value for velocity, so rearrange:


Velocity = \frac {Distance} {Time}


So we need now to find the distnace traveled, and the time it takes. Let's call the width of the garden W. Then the total distance traveled is 2*W, so that's the numerator. Now you need to figure out how long the total trip took to complete - which is the sum of the time for the trip over plus the trip back. The time for each segment of the cat's journey is found using the formula time = distance/velocity; do you see how I got that? So the trip over takes W/240, and the trip back took W/160, and the total time is W/240 + W/160. Now you can find the average speed:


V = \frac { 2*W} {\frac W {240} + \frac W {160}}


See how the W terms cancel out? Can you take it from here, and post back the final answer that you get?

Remember the basic equation of velocity:


Distance = Velocity \ *\ Time


Here we want to find the value for velocity, so rearrange:


Velocity = \frac {Distance} {Time}


So we need now to find the distnace traveled, and the time it takes. Let's call the width of the garden W. Then the total distance traveled is 2*W, so that's the numerator. Now you need to figure out how long the total trip took to complete - which is the sum of the time for the trip over plus the trip back. The time for each segment of the cat's journey is found using the formula time = distance/velocity; do you see how I got that? So the trip over takes W/240, and the trip back took W/160, and the total time is W/240 + W/160. Now you can find the average speed:


V = \frac { 2*W} {\frac W {240} + \frac W {160}}


See how the W terms cancel out? Can you take it from here, and post back the final answer that you get?

The average speed is 200 meters I think?

Nope, try again.

Simplify the fraction just below there;

\frac{2W}{\frac{160W + 240W}{(240)(160)}}

The average speed is 200 meters I think?

Sorry - that's incorect. You can't just average the two speeds. You can see why that doesn't work if you consider an easier case. Suppose you go 60 miles at 60 MPH, taking 1 hour of time. Then you cut your speed to 1 MPH and go another 60 miles - that will take another 60 hours, right? Total elapsed time is 1 hour + 60 hour= 61 hours, and total distance traveled is 2*60 = 120 miles. So your average speed is 120 miles/61 hours = 1.97 MPH. Compare that to simply averaging the speeds: (60+1)/2 = 30.5 MPH. Clearly averaging the speeds gets you the wrong answer.

Sorry - that's incorect. You can't just average the two speeds. You can see why that doesn't work if you consider an easier case. Suppose you go 60 miles at 60 MPH, taking 1 hour of time. Then you cut your speed to 1 MPH and go another 60 miles - that will take another 60 hours, right? Total elapsed time is 1 hour + 60 hour= 61 hours, and total distance traveled is 2*60 = 120 miles. So your average speed is 120 miles/61 hours = 1.97 MPH. Compare that to simply averaging the speeds: (60+1)/2 = 30.5 MPH. Clearly averaging the speeds gets you the wrong answer.

Ok thank you, I think I understand it now, is the answer 192?

Ah! That's it! Well done! :)

Ah! That's it! Well done! :)

Thank you for all your help :D xx