All of the above approaches are sound (and Patrick's was creative) but I just want to elaborate on thephoenix's:
rlative speed = 20-4=16miles/hr=4/15 miles/minute
in 5 minutes the cyclist cover a dis of 4/15*5 miles=4/3 miles
at a speed of 4miles / hour the hiker will need (4/3)/4 hour=1/3 hour=20 minute
Because they are travelling in the same direction, we can simply subtract the rates to find either the rate at which the faster object "catches up" to the slower one or, once caught up, the rate at which the faster object "exceeds" the slower one:
20 - 4 = 16
So, after passing the hiker, for 5 minutes the cyclist exceeds the hiker at a rate of 16mph.
Because 5 is just 1/12 of an hour, the cyclist has gained (1/12)*16 = 4/3 of a mile on the hiker (this is just distance = rate*time). Because we also know the hiker's rate, we can now use distance = rate*time again to solve for time, as thephoenix did.
TAKEAWAY:
When two objects travel in the
same direction, we can
subtract the rates.
When two objects travel in
opposite directions (meeting up or spreading apart), we can
add the rates.
Kaplan Teacher in Toronto
