Maths Problem

[JessUK98]

I'm working through an old Open University maths book (I want to do a 60 credit level 1 science module with them for fun starting October and thought I'd brush up on my maths).
I'm on a section where they are explaining the use of formulas and they use Naismith's Rule.

T = D/5 + H/600
where:
T = time to walk in hours
D = horizontal distance walked in km
H = height climbed in metres.

They gave an example of how long a walk will take if the horizontal distance is 20km and the height is 1200m
so:
T = 20/5 +1200/600 = 4 + 2 = 6 hours.

That's simple enough.

However they then give you one to work out yourself.
"Use Naismith's rule to estimate the time for a walk in which the horizontal distance is 5000m and the height is 500m"

Horizontal distance needs to be in km, so I convert: 5000m = 5km. Height is already in correct units
and I do the following:
T = 5/5 + 500/600 = 1 + 0.83 = 1.83


The solution they give though is;
T 5/5 + 500/600 = 1 5/6
so it takes 1hr 50 minutes

I don't get it? If I get my calculator to give my answer in a fraction it gives me 11\6
I get 5/6 if I just do 500/600 , but if I add 1 my calculator goes to 11/6.

[mike]

However they then give you one to work out yourself.
"Use Naismith's rule to estimate the time for a walk in which the horizontal distance is 5000m and the height is 500m"

Horizontal distance needs to be in km, so I convert: 5000m = 5km. Height is already in correct units
and I do the following:
T = 5/5 + 500/600 = 1 + 0.83 = 1.83


The solution they give though is;
T 5/5 + 500/600 = 1 5/6
so it takes 1hr 50 minutes

I don't get it? If I get my calculator to give my answer in a fraction it gives me 11\6
I get 5/6 if I just do 500/600 , but if I add 1 my calculator goes to 11/6.

All answers are equivalent

11/6 = 1-5/6 = 1.83 = 1 h 50 m

(5/6 + 1 = 5/6 + 6/6 = 11/6)

[PhaseThree]

The answer you get (1.83hr) is correct but this is a decimal value. No-one uses decimal time - even the French gave up on the idea. So you need to translate 1.83 hours to something usable. To do this you need to multiply the number of minutes in an hour by 0.83 (60 x0.83) which gives you 50. So the result in standard time format is 1hr 50 minutes.

[JessUK98]

Thanks both. Sounds so simple now