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My 10 year old granddaughter asked me to set her a really difficult maths question, so I made up some gobbledygook question about a fly and a flea flying in opposite directions, to which the joke answer was going to be 'fly past flea'.

Unbeknownst to me, my adult daughter thought it was a serious question and texed it to her maths whizz work colleague who spent ages working it out. Then, proud as punch he sent her the answer, an explanation of how he worked it out, and a photo of his notebook.

Now he wants me to confirm that he is correct. I of course have no idea so some help would be appreciated.

This is what Bridie sent him.

Fly flies from London to Brighton at 26mph 117 miles away  gets there at 1pm
Flea goes from Brighton to London 36mph gets there at 12:30pm

What time do they meet?

Fly left London at 08:30.
Flea left Brighton at 09:15.

At 09:15 the Fly had flown 19.5 miles therefore distance left between fly and flea was 97.5 miles.

Closing speed was 62mph, at which speed it would take 1h 34m 21.3s to cover the 97.5 miles so they met at 10:49:21.

I think.

It must have flown a very erratic flight path, Brighton is only about 55 miles from Central London.

Thanks. This is his answer. I'm so impressed with both of you. I could never have done it.



So I worked out what time they both left.
Then worked out their speeds (top).
Then worked out where the fly would be when the flea left.
Then worked out the distance left for the fly.
Then used the ratio 26:36 or 26/62 to work out the mileage that they would fly before meeting (40.89 miles).
Added that tho the 19.5 miles the fly already did (60.387).
The worked out this would take him 2.3225 hours (60.387/26).
Which is 139.35 mins.
Which is 2 hours 19 mins and about 21 seconds.
I then added this to the starting time of 8:30 to get 10:49:21. :)

This

Was the flea on a plane?