Ella and Sian have cycled 16 km from home, when the back wheel of Ella's bicycle falls of so they decide to set off for home, leaving her bike secured on a tree.They agree Sian rides the bike first and leaves the bike for Ella when she arrives and Ella rides the bike while Sian walks the rest.Ella walks at 4 km per hour and cycles 10 km per hour. Sian walks at 5 km per hour and cycles at 12 km per hour. For what length of time should Sian ride the bike, so that both arrive home.
+129849 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........
