Page 54 - Algebra 1

5.
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
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= –
4=1 𝑥 60
11
10 15
4q = 1 30
120=1 =y 𝑞
4+6=1 𝑥 𝑦 15
4+6=1 𝑥 120 15
4+1=1 𝑥 20 15
411
=–
𝑥 15 20
x = 240 days
The women will take 240 days to complete the work when working alone.
Page 53 of 54
ALGEBRA