SOLUTION: 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

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
RELATED QUESTIONS
Jack and Jill walked along a level road, up the hill, back (along the same path) down the (answered by Alan3354,fractalier)

jack and jill are hired to empty a tank. if they work together it takes them 12 minutes.... (answered by mananth)

Jack and Jill are hired to empty a tank. If they work together it takes them 12 minutes.... (answered by nerdybill)

Jack and Jill went up the hill at a rate of 8 units per minute.... (answered by ankor@dixie-net.com)

Jack and Jill went up the hill at a rate of 8 units per minute. They came tumbling down... (answered by josgarithmetic)

Jack and Jill went up the hill at 8 units per minute and came tumbling down the hill at 8 (answered by josgarithmetic)

Jack is driving at a speed that is 5 mph faster than Jill is driving. Jack drives 432... (answered by Alan3354)

Jack and Jill each own a collection of mp3 files. Jill has six mp3 files less than three... (answered by lwsshak3)

7 people are seated around a table. What is the probability that Jack and Jill are not... (answered by AnlytcPhil,Alan3354)