The question that you were set was about a hairdryer with two heating wire coils in parallel. The first part about calculating the length of the wire went well. It was 3 metres. You then calculated the power of R1 which was 300 Watts (to 1 sig fig)
In the second part, it said that wire 2 was then connected in parallel and there was 3 x the power used.
This is the easy way to solve it.
Three times the power means a combined output of 900 Watts. But R1 is already giving out 300 Watts so R2 must give out 600 Watts.
R2 on its own has twice the power of R1, but the supply voltage is the same.
P=IV
So twice the power means twice the current.
If twice as much current is getting through, then wire 2 must have half the resistance.
Half the resistance means half the length.
Wire 2 is 1.5 metres.
