# Forth and back

Car drive from point A to point B at a speed of 78 km/h and back at 82 km/h. If I went there and back at a speed of 81 km/h journey would take five minutes less. What is the distance between points A and B?

x =  256.9821 km

### Step-by-step explanation:

x = 78a
x = 82b
2x = 81(a+b-5/60)

x = 78·a
x = 82·b
2·x = 81·(a+b-5/60)

78a-x = 0
82b-x = 0
4860a+4860b-120x = 405

Pivot: Row 1 ↔ Row 3
4860a+4860b-120x = 405
82b-x = 0
78a-x = 0

Row 3 - 78/4860 · Row 1 → Row 3
4860a+4860b-120x = 405
82b-x = 0
-78b+0.926x = -6.5

Row 3 - -78/82 · Row 2 → Row 3
4860a+4860b-120x = 405
82b-x = 0
-0.025x = -6.5

x = -6.5/-0.02529359 = 256.98214286
b = 0+x/82 = 0+256.98214286/82 = 3.13392857
a = 405-4860b+120x/4860 = 405-4860 · 3.13392857+120 · 256.98214286/4860 = 3.29464286

a = 369/112 ≈ 3.294643
b = 351/112 ≈ 3.133929
x = 14391/56 ≈ 256.982143

Our linear equations calculator calculates it. Did you find an error or inaccuracy? Feel free to write us. Thank you!

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