If Gideon had driven for 20 minutes less than the time he would have driven if he had driven 20 kilometers less than he did drive but at two-thirds the speed at which he drove, he would have driven 10 kilometers less than he did.

However, if he had driven 20 minutes longer than the time he would have driven if he had driven 10 kilometers less than he did drive but at three-quarters the speed at which he drove, he would have driven 20 kilometers further.

How far did Gideon drive?

Let d be the actual distance (km).
Let s be the actual speed (km/hr).

20 min = 1/3 hr.

((d-20)/(2s/3) - 1/3) s = d - 10

and

((d-10)/(3s/4) + 1/3) s = d + 20

From the first:

3s(d-20)/(2s) - s/3 = d - 10
3d/2 - 30 - s/3 = d - 10
9d - 180 - 2s = 6d - 60
3d = 2s + 120

From the second

4s(d - 10)/(3s) + s/3 = d + 20
4d/3 - 40/3 + s/3 = d + 20
4d - 40 + s = 3d + 60
d = 100 - s
3d = 300 - 3s

2s + 120 = 300 - 3s
5s = 180

s = 36
d = 64

 

Posted by Charlie on 2007-05-15 15:56:02