There were many correct answers sent in for this problem. As Primary Maths Club (International School of Toulouse) pointed out, it helps if you start counting seconds from the first time the two lights flashed together (at zero seconds).

Some people thought about a number line, others looked for a number that both of the numbers of seconds (4 and 5) would divide into (common multiple). Here are two very well explained solutions:

Holly West, Harriette Arkle, Caroline Anderton, Florence Marsden & Rebecca Bartram (Age 11/12, The Mount School, York).

"1st light 0 - 4 - 8 - 12 - 16 - 20 - 24 - ......
2nd light 0 - 5 - 10 - 15 - 20 - 25 - ........

They flash at the same time every 20 seconds 0 - 20 - 40 - 60
That's four times in all.

For two lights the pattern was every 20 seconds and 4 x 5 = 20
For the three lights it is going to be 4 x 5 x 7 = 140 seconds or 2 minutes 20 seconds"

Christina Ivanova (Age 11, Marlborough Primary School)

"To work this out you need to find a multiple of both 5 and 4 which is 20. So the lights flash together every 20 seconds and to find out how many times they flash in one minute you need to do 60 ÷ 20 = 3 which means that they flash together 3 times a minute.

You need to find a multiple of 20 and seven to work out how many minutes before all of the lights flash together. 20 x 7 = 140 sec = 2 mins 20 sec"

Well done to all of the following people:
Jesse Allen, Edward Quantrill, Daniel Vinnicombe (Age 10) and Thomas Harley (Age 9, Tattingstone School) who did some very good work with finding the multiples. Lily Moore (Age 12, Sotogrande International School) Daniel Loh (Age 10, Anglo-Chinese School, Singapore), Abigail Smith (Age 9), Charles Poole and David Bailey (Age 10, Moorgate Primary School, Staffordshire), Jason Day (Priory School), Thomas Robinson (St Francis School, Maldon) and Ashley.