Question 1141306: Jack and Jill start walking up a hill together. Jack reaches the top 90 minutes before Jill. On the way down, Jill calculated that, if she had walked 50% faster and Jack had walked 50% slower, then they would have arrived at the top together. How long did it take Jill to reach the top of the hill?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Jack and Jill start walking up a hill together.
Jack reaches the top 90 minutes before Jill.
On the way down, Jill calculated that, if she had walked 50% faster and Jack had walked 50% slower, then they would have arrived at the top together.
How long did it take Jill to reach the top of the hill?
:
let a = Jack's speed
let b = Jill's speed
let t = Jack's time to the top of the hill
then
(t+90) = Jill's time to the top of the hill
:
write a dist equation; dist = speed * time
at = b(t+90)
:
"Jill calculated that, if she had walked 50% faster and Jack had walked 50% slower, then they would have arrived at the top together. "
.5at = 1.5bt
.5a = 1.5b
a = 3b
:
in the 1st equation, replace a with 3b
3bt = b(t+90)
3bt = bt + 90b
3bt - bt = 90b
2bt = 90b
divide both sides by 2b
t = 45 min
:
" How long did it take Jill to reach the top of the hill?"
45 + 90 = 135 min
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