“A man left home at 11.30 a.m. and cycled 5 miles to a railway station at the rate of 12 miles an hour. He waited 10 minutes at the station and then travelled by train a distance of 36 miles at the rate of 24 miles an hour. At what time did he reach his destination?”

What they did not show as usual was how to get to the answer.  So here goes:

Start – 11.30 a.m.

cycled to the station 5 miles at 12 miles in 1 hour, or 12 miles in 60 min.  This is the same as saying 1 mile in 60/12 minutes or 5 minutes. So he will do 5 miles in 25 minutes.

He waits for 10 minutes.

Travels by train 36 miles at 24 miles an hour or 24 miles in 60 minute .  This is the same as saying 2 miles in 5 minutes [dividing by 12 a common factor of 24 and 60] .   He will travel 36 miles [ 2 x 18 ] in 18 x 5 or 90 minues.

So the total time from the time he started would be 25 + 10 + 90 minutes or 125 minues.  1 hour is 60 minutes so 125 minutes is 2 hours and 5 minutes.

So he arrives at 11.30 —- 1 hour —> 12.30 —– 1 hour —-> 1.30 p.m — 5 minutes —> 1.35 p.m.

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