Forth and back

Car drive 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 answer:

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!







Tips for related online calculators
Looking for calculator of harmonic mean?
Looking for a statistical calculator?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Do you want to convert velocity (speed) units?
Do you want to convert time units like minutes to seconds?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions: