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Jason from Priory Middle School, Dunstable says:

The time where the 2 watches are 10 mins apart is 9:20.

At 7 o'clock they're 3 mins apart
At 8 o'clock they're 6 mins apart
9 o'clock, 9 mins.
For 1 minute you divide 1 hour by 3, as 20 is 3 times as small as 60.
Then you add 9:00 and 0:20 to make 9:20, which is when they are 10 mins apart.

Stuart and Mark (Lower Juniors at Cummersdale, Cumbria) also say 9:20. They used this technique:

Every hour the difference between the two watches increases by 3 minutes 3x3=9
That gives us 3 hours and then divide 60 into 3 to make 20 minutes
3hours + 20mins = 3 20mins
6:00 a.m. + 3hrs 20 mins = 9:20 a.m.

George (Rosebank Primary School, Leeds) drew diagrams to show his thinking:

I knew that it would take them 3 hours and something because every hour they got three minutes apart. That meant that it will have minutes as well as hours. I knew that Mandeep's and Adam's watches went three minutes apart every hour. Now I needed to know how many minutes apart the boys' watches go in one minute. For this I drew a scale.

Then I marked how much they'd be apart.

This showed me that it must be between 15 and 30 minutes. When I divided it into even smaller parts I got the answer.

This got me to the answer, which is 3 hours and twenty minutes.

Daniel (Anglo-Chinese School - Primary, Singapore), Thomas (Tattingstone School) and Timothy (Munsang College, Hong Kong) gave very similar explanations. The one below is Timothy's:

Mandeep's watch loses 2 min every hour and Adam's watch gains 1 min every hour,
so they are 1 + 2 = 3 min apart after the 1st hour and 3 more mins after every hour.
When they arrive at the airport, their watches are 10 mins apart, so they travel:
10/3 hours = 60 x 10/3 = 200min = 3hours and 20mins
They start at 6:00am, so they arrive at 9:20am.

Tyler from Ysgol Dyffryn Dulas wrote:
Mandeep's watch has 58 mins per hour, I timesed that by 3 = 174
I did the same with 61, Adams' watch, 183
Now the difference was 9 mins
I timesed 58 by a third =19 and the same with 61=20
Now the difference was 1 minute
9+1=10 I had found the answer
Then I converted them to hours:  3:13, 3:23 from here I woked out as 7, the difference beetween 3:13 and 3:20 was 3, the difference beetween 3:20 and 3:23 was 7, which was roughly double 3.
3:20+6:00 was the answer to complete the soloution and that answer was 9:20 there for they arrived at 9:20.