a boy rode his bicycle northward, then turned left and rode 1 km and again turned left and rode 2 km. he found himself 1 km west of his starting point. how far did he ride northward initially?

June 28, 2026

He rode 2 km northward initially.

Step-by-step reasoning

Let’s imagine the boy’s path on a simple grid.

Let his starting point be OOO.
He rides straight north xxx km to point AAA.
From facing north, a left turn means going west.
He rides 1 km west to point BBB.
From facing west, another left turn means going south.
He rides 2 km south to point CCC.

Now use the condition:

Final position CCC is 1 km west of the starting point OOO, i.e. horizontally 1 km left of OOO, but vertically at the same level as OOO.

Assigning coordinates:

O=(0,0)O=(0,0)O=(0,0)
After going north xxx km: A=(0,x)A=(0,x)A=(0,x)
After going 1 km west: B=(−1,x)B=(-1,x)B=(−1,x)
After going 2 km south: C=(−1,x−2)C=(-1,x-2)C=(−1,x−2)

Since CCC is 1 km west of OOO, its coordinates must be (−1,0)(-1,0)(−1,0). So we set:

x−2=0⇒x=2x-2=0\Rightarrow x=2x−2=0⇒x=2

Therefore, he rode 2 km northward initially.

Forum-style quick answer

A boy rode his bicycle northward, turned left for 1 km, then left again for 2 km, and ended 1 km west of where he started.
How far did he go north at first?

Represent the path on a coordinate grid.
Write the final coordinates using the unknown northward distance xxx.
Use the “1 km west of start” condition to get the equation x−2=0x-2=0x−2=0.
Solve to get x=2x=2x=2 km.

Final: He initially rode 2 km north. ✅ TL;DR: Draw it on a grid, track coordinates, and you get x=2x=2x=2 km for the initial northward ride.