It took Jack 15 minutes to walk up to the top of the hill.
Let v = Jill's speed and v' = Jack's speed. Let t = time it takes Jill to walk up to the top of the hill, since Jill arrives 10 minutes earlier, Jack's time, t' = t + 10.
Since the distance covered by both Jack and Jill is the same, we have that
vt = v't'
vt = v'(t + 10)
Since Jack calculated that if he walked 50 % slower and Jill 50 % faster, they would arrived at the top at the same time, Jack's new speed is V = v' + 0.5v'. (since there is a 50 % increase in speed).
Also, Jill's new speed is V' = v - 0.5v (since there is a 50 % decrease in speed)
Since they both arrive at the top at the same time, T, and the distance covered is equal, we have that VT = V'T
(v' + 0.5v')T = (v - 0.5v)T
1.5v' = 0.5v
v'/v = 1.5/0.5
v'/v = 3
From (1)
vt = v'(t + 10)
(v'/v)t = t + 10
3t = t + 10
3t - t = 10
2t = 10
t = 5 minutes
Since Jack's time t' = t + 10, substituting t = 5 into the equation, we have
t' = t + 10
= 5 + 10
= 15 minutes
So, it took Jack 15 minutes to walk up to the top of the hill.
Learn more about time of travel here:
brainly.com/question/12190190