Cyclist

The cyclist rode two-fifths of the way the first day. On the second day drove 5 km less while traveling three-eighths of the route. How many kilometers does he have to finish the target?

Correct answer:

x =  45 km

Step-by-step explanation:


a = 2/5 t
b = a-5
b = 3/8 t
x = t - a - b

a = 2/5·t
b = a-5
b = 3/8·t
x = t - a - b

5a-2t = 0
a-b = 5
8b-3t = 0
a+b-t+x = 0

Row 2 - 1/5 · Row 1 → Row 2
5a-2t = 0
-b+0.4t = 5
8b-3t = 0
a+b-t+x = 0

Row 4 - 1/5 · Row 1 → Row 4
5a-2t = 0
-b+0.4t = 5
8b-3t = 0
b-0.6t+x = 0

Pivot: Row 2 ↔ Row 3
5a-2t = 0
8b-3t = 0
-b+0.4t = 5
b-0.6t+x = 0

Row 3 - -1/8 · Row 2 → Row 3
5a-2t = 0
8b-3t = 0
0.025t = 5
b-0.6t+x = 0

Row 4 - 1/8 · Row 2 → Row 4
5a-2t = 0
8b-3t = 0
0.025t = 5
-0.225t+x = 0

Pivot: Row 3 ↔ Row 4
5a-2t = 0
8b-3t = 0
-0.225t+x = 0
0.025t = 5

Row 4 - 0.025/-0.225 · Row 3 → Row 4
5a-2t = 0
8b-3t = 0
-0.225t+x = 0
0.1111x = 5


x = 5/0.11111111 = 45
t = 0-x/-0.225 = 0-45/-0.225 = 200
b = 0+3t/8 = 0+3 · 200/8 = 75
a = 0+2t/5 = 0+2 · 200/5 = 80

a = 80
b = 75
t = 200
x = 45

Our linear equations calculator calculates it.

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.
Do you have a system of equations and are looking for calculator system of linear equations?
Do you want to convert length units?

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

Units of physical quantities:

Themes, topics:

Grade of the word problem:

Related math problems and questions: