SOLUTION: Bill sets out to drive from Swansea to London. An hour after he'd started, he encountered heavy traffic and he was only able to drive at three-fifths of his former speed. He event

Question 726238: Bill sets out to drive from Swansea to London. An hour after he'd started, he encountered heavy traffic and he was only able to drive at three-fifths of his former speed. He eventually arrived in London two hours later than he'd expected, and worked out that if he'd not met traffic until fifty miles further on he would have arrived in London forty minutes sooner. How far is it from Swansea to London?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Bill sets out to drive from Swansea to London.
An hour after he'd started, he encountered heavy traffic and he was only able to drive at three-fifths of his former speed.
let s = his normal speed
then
.6s = his heavy traffic speed
and
let d = the distance from Swansea to London
He eventually arrived in London two hours later than he'd expected,
Write a time equation of this scenario
1 + = + 2
multiply by .6s, resulting in:
.6s + (d-s) = .6d + .6s(2)
.6s - s + d = .6d + 1.2s
-.4s + d = .6d + 1.2s
d - .6d = 1.2s + .4s
.4d = 1.6s
d =
d = 4s
:
and worked out that if he'd not met traffic until fifty miles further on he would have arrived in London forty minutes sooner.
That means he would only be 1 hr and 20 min late, 4/3 hr
1 + + = +
Multiply by 3s
3s + 3(50) + 5(d-s-50) = 3d + 4s
3s + 150 + 5d - 5s - 250 = 3d + 4s
combine like terms
3s - 5s - 4s + 150 - 250 = 3d - 5d
-6s - 100 = -2d
6s + 100 = 2d, mult by -1
simplify divide by 2
3s + 50 = d
replace d with 4s
3s + 50 = 4s
50 = 4s - 3s
s = 50 mph is the speed
then
4(50) = 200 mi from Swansea to London

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