Page 51 - Algebra

4.
Let s be the speed of Julie
t is the original time taken
d is the distance between home and school.
d = st
When she walks faster,
Speed = s + 2
Time = t – 4
Distance = (s + 2) (t – 4)
st = (s + 2) (t – 4)
st = st –4s + 2t – 8
4s – 2t = –8.....................(1)
When she walks slower,
Speed = s – 4
Time = t + 12
Distance = (s – 4) (t + 12)
st = (s – 4) (t + 12)
st = st + 12s – 4t – 48
– 12s + 4t = –48
– 3s + t = –12.....................(2)
Multiply (2) with 2
– 6s + 2t = –24
Add (1)
– 2s = – 32
s = 16 km
5.
Let x be the time taken by the women
y be the time taken by the girl
4+6=1 𝑥 𝑦 15
Put1 =p,1 =q 𝑥𝑦
1
4p + 6q = 15............ (1)
2+5=1 𝑥 𝑦 20
2p + 5q = 1 20
Multiply by 2
1
4p + 10q = 10...........(2)
(2) – (1)
4q = –
11
10 15
4q = 1 30
120=1 =y 𝑞
4+6=1 𝑥 𝑦 15
Page 50 of 177
Algebra I & II