This is analogous to a distance-time-speed problem. Of course, you don't need to see it that way to solve the question but I think it's just good to be aware how you can relate concepts that are seemingly different.

H -> ................ <- S

Now the question can be understood in the following manner: H moves at 7 km/hr and S moves at 3 km/hr. When they meet, how much of the distance has S covered? Let's assume the distance is 21 km (divisible by both 3 and 7, probably your first instinct as a number). Recall when they meet, the time taken for both is equal

x / 7 = (21 - x) / 3

(At this point you will recognize that choosing a small number like 1 will probably be better than 21)

x = 14.7

So H covers 14.7 km, which means S covers 6.3 km.

The distance S covered as a ratio is 6.3 / 21 = 63 / 210 = 0.3. Again, this calculation is much quicker if you are smart with picking a distance value.

Probably not the quickest method, just the method I used.

Explanation

You don’t know how many trees there are, so define the job by plugging in an easy number, such as 21 trees.

Use rate pies to figure out that Helen’s rate is 7 trees/hr and Sergey’s rate is 3 trees/hr. That means their combined rate is 10 trees/hr. Put their combined rate into another
rate pie with the total trees to find it takes them \(\frac{21}{10}\) or 2.1 hours to meet.

To find out how many trees Sergey has cut down at this point, put his individual rate into another rate pie with 2.1 hours. 3 trees/hr × 2.1 hours = 6.3 trees at the point they meet. Put the number of trees Sergey has cut when they meet over the total trees: \(\frac{63}{21}=\frac{3}{10}\), so the correct answer is \(\frac{3}{10}\) or 0.3.

just a little correction ans has 10/3 instead of 3/10

Fixed. Precious.

Regards

Rate of Helen 1/3 trees per hr

Sergey 1/7 trees per hour

Together rate 10/21

Serger have cut= 21/10*1/7=

Answer - 3/10 trees

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