Mmmmmm....this looks interesting !!!
I'm assuming that the problem is supposed to have stated that they arrived home at the same time....
Let Sian's time on the bike [in hours] = S
So the distance he rides = rate * time = 12S
So....the distance he walks = 16 - 12S
Call Ella's time on the bicycle (in hours) = E
And the distance that she rides = rate * time = 10E
And the distance that Ella rides = Sian's walking distance
So.....10E = 16 - 12S
So E = [16 - 12S] / 10
And Sian's walking distance / his walking rate = the time he walked = [16 - 12S] / 5
And Ella's walking distance / her walking rate = the time she walked = [16 - 10E] / 4 =
the distance that Sian rdes/ her walking rate = 12S / 4 = 3S
And since they begin and end at the same time....
The total time that Sian rode + the time he walked = the total time that Ella walked + the time she rode ......so we have....
S + [16 - 12S] / 5 = 3S + [16 - 12S]/10
-2S = ( [16 - 12S] - 2[16 - 12S] ) / 10
-20S = 16 - 12S - 32 + 24S
-20S = -16 +12S
-32S = -16 divide both sides by -32
S = -16/-32
S = 1/2 [hours] = 30 minutes = Sian's time on the bike.... [just as Solveit predicted.....!!! ]
Note that each travels for 2.5 hours........
