Two tractors working together cultivated 2 3 of a field in 4 days. How long would it take each tractor to cultivate the whole field by itself if the first tractor can do the job 5 days faster than the second?
This are my weak type of problems. can someone show me a detailed solution so i can memorize the "formula" . thx
I'll answer a related question.
It takes Alice 2 hours to dig a hole, and Bob 3 hours to dig a hole. How long if they work together?
OK. The trick is to identify the variable that will allow you to solve this. Here it is the speed of hole-digging, or, better, rate of hole digging. It's quite hard to spot when you first try these problems, but they are often based around rates.
The rate at which Alice digs a hole is $1/2$ holes per hour. The rate at which Bob digs is $1/3$ holes per hour. Their combined rate is $1/2+1/3=5/6$ holes per hour. In one hour, they dig $5/6$ of a hole.
How many hours are needed per hole? This is just the reciprocal ("1 over...") of the rate, $1/(5/6)=6/5$ hours, or 1 hour 12 minutes.
In your tractor question, we can call the first tractor's rate of doing work $x$, and the second $y$. The units could be fields plowed per day. How long would it take both tractors to completely plow a field? What equation could we set up given the information in the second sentence?