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aloeverahe · Feb 23, 2009, 03:05 AM

Can someone help find the equation for this question, the rest i might be able to do afterwards...

A man cycled a distance of $L$ km in $n$ hours. For part of the time he cycled a $u$ km/h and for the rest at $v$ km/h. For how long did he cycle at $u$ km/h? Give the answer in its simplest for in terms of $L, n, u and v$

do you use x and y for this question, because if you do, would: $xu + yv = L$ work?

or if you don't add x and y, would it be: $(u+v)n=L$ , which therefore ends up as [math] distance = u=L/n-v[/maths]?

I just want the equation, unless you are willing to give me working out to the equation, then thank you so much!!

sarnian · Feb 23, 2009, 03:50 AM

Hello Aloeverahe (hmmmm : nice soft skin there ;) )

As there are two speeds (u and v) with different periods, you have to add L(u) + L(v) to get the total L.
You should use x for speed u and y for speed v, as these periods are unknown.

L(u) = ux , and L(v) = vy
L(u) + L(v) = L
ux + vy = L
ux = L - vy

You want to know the value of x :

x = (L - vy)/u

Note that you used Km/hr for speed, so your time is in hours too.

(u+v)n = L is incorrect as you add here u and v, making the speed higher than either one of them, times the total time period.