Answer
The time taken by first welder is $26\;hours$
and the second welder is $22\; hours$.
Work Step by Step
Let the first welder worked $x\;hours$.
and the second welder worked $y\;hours$.
Total time on a project $=48\;h$.
$\Rightarrow x+y=48$ ...... (1)
The gross earnings $=\$1734$.
$\Rightarrow 32x+41y=1734$ ...... (2)
Multiply equation (1) by $-32$.
$\Rightarrow -32x-32y=-1536$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 32x+41y-32x-32y=1734-1536$
Simplify.
$\Rightarrow 9y=198$
Divide both sides by $9$.
$\Rightarrow y=22$
Substitute the value of $y$ into equation (1).
$\Rightarrow x+22=48$
Subtract $22$ form both sides.
$\Rightarrow x=48-22$
Simplify.
$\Rightarrow x=26$
Hence, the time taken by first welder is $26\;hours$ and by the second welder is $22\; hours$.
