I'm having an entrance examination in two days and I'm having problems with this math problem here.
A group of workers works on two jobs in two days. The second job is 2 times smaller in volume than the first one. The first day till midday the workers work on the first job, then afternoon half of the group of workers stays at the first job and finishes it, the second group is switching to the second job. The second day one worker from that group finishes the second job while working on it for the whole day. How many workers are there in the group ?
The answer is 8, but I don't know how to get to that answer. If anybody could help me with this problem step by step and if someone could give me some tips and advice on how to approach any text problem. Thank you :D
Let $x$ denote the number of workers.
Define working day as the amount of work done by one worker in one day.
The first job was completed within $x\cdot\frac12+x\cdot\frac12\cdot\frac12=\color\red{\frac34x}$ working days.
The second job was completed within $x\cdot\frac12\cdot\frac12+1=\color\green{\frac14x+1}$ working days.
Since the second job is $2$ times smaller than the first job, $\color\red{\frac34x}=2\cdot(\color\green{\frac14x+1})$:
$\frac34x=2\cdot(\frac14x+1)\implies$
$\frac34x=\frac24x+2\implies$
$\frac14x=2\implies$
$x=8$