SOLUTION: Paul and James go out for a cycle and are 16 km from home when Paul runs into a tree damaging his bicycle beyond repair. They decide to return home and that Paul will start on foot

Question 696394: Paul and James go out for a cycle and are 16 km from home when Paul runs into a tree damaging his bicycle beyond repair. They decide to return home and that Paul will start on foot and James will start on his bicycle. After some time, James will leave his bicycle beside the road and continue on foot, so that when Paul reaches the bicycle he can mount it and cycle the rest of the distance. Paul walks at 4 km/h and cycles at 10 km/h, while James walks at 5 km/h and cycles at 12 km/h. For what length of time should James ride the bicycle, if they are both to arrive home at the same time?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Paul and James go out for a cycle and are 16 km from home when Paul runs into a tree damaging his bicycle beyond repair.
They decide to return home and that Paul will start on foot and James will start on his bicycle.
After some time, James will leave his bicycle beside the road and continue on foot, so that when Paul reaches the bicycle he can mount it and cycle the rest of the distance.
Paul walks at 4 km/h and cycles at 10 km/h,
while James walks at 5 km/h and cycles at 12 km/h.
For what length of time should James ride the bicycle, if they are both to arrive home at the same time?
:
We know that while one is riding the other is walking and vice-versa
:
Let x = James riding time, this is also Paul's walking time
Let y = Paul's riding time, this also James walking time
:
Write a distance equation for each guy
James: 12x + 5y = 16
Paul: 4x + 10y = 16
:
multiply the 1st equation by 2, subtract the 2nd
24x + 10y = 32
4x + 10y = 16
-----------------
20x = 16
x = 16/20
x = .8 hrs James's time riding
:
Both will take .8 + 1.28 = 2.08 hrs to complete the trip of 16 km
:
To check this, find y using the 2nd equation 4x + 10y = 16
4(.8) + 10y = 16
3.2 + 10y = 16
10y = 16 - 3.2
10y = 12.8
y = 12.8/10
y = 1.28 hrs
:
Check this in the James equation
12(.8) + 5(1.28) =
9.6 + 6.4 = 16 mi
and in the Paul's equation
4(.8) + 10(1.28) =
3.2 + 12.8 = 16 mi; confirms our solution of James riding for .8 hrs
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