Forth and back

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

Correct result:

x =  256.9821 km

Solution:


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

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

Our linear equations calculator calculates it.



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