to solve this question, i'll make a sketch on their positions
the first bicyclist travels at 8mph. The second bicyclist travels at 12mph but departure time was exactly 1hr behind the first cyclist.
we can clearly say that the first cyclist has travelled 8 miles after one hour (assuming he travelled at constant acceleration).
the second cyclist picks up and travels after 1 hr maintaining a constant acceleration
let A represent cyclist 1
let B represent cyclist 2
after second hour
A = (8 + 8) miles = 16 miles
B = 12miles
third hour
A = (8 + 8 + 8)miles =24miles
B = (12 + 12) = 24 miles
now their miles apart = 24 + 24 = 48 miles apart
fourth hour
A = (8 + 8 + 8 + 8) = 32 miles
B = (12 + 12 + 12) = 36 miles
total miles apart = 32 + 36 = 68 miles
note: we didn't start counting hourly at the exact time A started journey but rather when the journey started for both of them which includes A (first cyclist).
since they are 68 miles apart, it takes A four hours onthe road and B (4 -1 = 3 hours)
the second cyclist have travelled for 3 hours when they're 68 miles apart
