Cyclist 25591

The cyclist rode 44 km and 400 m in three days. In the first hour, he covered the course 5% longer than in the second hour, and in the third hour, he covered 1 km more than in the first hour. How many km did he travel in the third hour?

Correct answer:

c =  15.7 km

Step-by-step explanation:


a+b+c = 44+400/1000
a = b + 0.05b
c = 1 + a

a+b+c = 44+400/1000
a = b + 0.05·b
c = 1 + a

1000a+1000b+1000c = 44400
a-1.05b = 0
a-c = -1

Row 2 - 1/1000 · Row 1 → Row 2
1000a+1000b+1000c = 44400
-2.05b-c = -44.4
a-c = -1

Row 3 - 1/1000 · Row 1 → Row 3
1000a+1000b+1000c = 44400
-2.05b-c = -44.4
-b-2c = -45.4

Row 3 - -1/-2.05 · Row 2 → Row 3
1000a+1000b+1000c = 44400
-2.05b-c = -44.4
-1.512c = -23.741


c = -23.74146341/-1.51219512 = 15.7
b = -44.4+c/-2.05 = -44.4+15.7/-2.05 = 14
a = 44400-1000b-1000c/1000 = 44400-1000 · 14-1000 · 15.7/1000 = 14.7

a = 147/10 = 14.7
b = 14
c = 157/10 = 15.7

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