# Tyre Question

Can someone please explain what the markscheme has done for this question for part a and b, as I don't seem to understand it at all?

I get when they minus the tread depth as the circumference for each rotation will be smaller, but other than that I am pretty lost.

For example, in b) why do they minus 8.5 then add 1.6?

Any help greatly appreciated.

You could think of the distance travelled in an hour. The number of revolutions is the same for the two different tyres and the circumference is proportional to the diameter(s). So the new speed (distance travelled) will be (roughly) 607/621 of the old speed.

Its worth being clear about their reasoning, but just thinking about proportionality and ratios is simpler.
(edited 2 months ago)
Oh so smth like this?

I don't really then get the example given in part a then.
If the speedometer shows 80mph, shouldnt the actual speed be ~78mph not 70?
Original post by mosaurlodon
Oh so smth like this?

I don't really then get the example given in part a then.
If the speedometer shows 80mph, shouldnt the actual speed be ~78mph not 70?

For the 70/80 example, its hypothetical to make it clear that if wheels are smaller and they rotate at the same rate as normal wheels, then the linear speed of the car will be smaller.

But yes for the ratio, though youd need to justify it so
linear speed = circumference * rotational speed
= pi*607 * 70 / (pi*621)
with all the appropriate/tedious units conversions. But its easier to just use proportionality as long as its justified.
(edited 2 months ago)
oh so they just like made that up?
Also I don't really get how the ms allows 621.5-8.5+1.6/621.5, surely if you misinterpret the diameter as the radius, you would get a much more skewed ratio?
But then again the final answer seems to be close enough so maybe the difference is just relatively negligible?
Original post by mosaurlodon
oh so they just like made that up?
Also I don't really get how the ms allows 621.5-8.5+1.6/621.5, surely if you misinterpret the diameter as the radius, you would get a much more skewed ratio?
But then again the final answer seems to be close enough so maybe the difference is just relatively negligible?

Im guessing this is a mark scheme so as 12a) is an explain, you wont have done the calculation yet (1 mark?), so they just want to get you thinking about the problem in the right way.

For the last part, Im guessing theyre not penalising the solution if the student inteprets the tyre diameter as the radius, which seems a bit odd, but I guess theyre being generous in exam conditions. However car tyres of 1.2m diameter would be on the large side.
(edited 2 months ago)
Ok I see, thank you very much for your help, I finally get this question