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 ukm/h and for the rest at vkm/h. For how long did he cycle at ukm/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!!

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.