# Destination 5286

Daniel reached the destination in 3 hours. Peter came to this place in 4.5 hours. What speed was Daniel moving if we know that Daniel's speed was 30 km/h faster than Peter's, and they both started at the same time from the same place?

d =  90 km/h

### Step-by-step explanation:

d = 30+p
s = 3d
s = 4.5p

d = 30+p
s = 3·d
s = 4.5·p

d-p = 30
3d-s = 0
4.5p-s = 0

Pivot: Row 1 ↔ Row 2
3d-s = 0
d-p = 30
4.5p-s = 0

Row 2 - 1/3 · Row 1 → Row 2
3d-s = 0
-p+0.333s = 30
4.5p-s = 0

Pivot: Row 2 ↔ Row 3
3d-s = 0
4.5p-s = 0
-p+0.333s = 30

Row 3 - -1/4.5 · Row 2 → Row 3
3d-s = 0
4.5p-s = 0
0.111s = 30

s = 30/0.11111111 = 270
p = 0+s/4.5 = 0+270/4.5 = 60
d = 0+s/3 = 0+270/3 = 90

d = 90
p = 60
s = 270

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