A hiker walking at a constant rate of 4mph is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20mph. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the bike catches up?
A. 6 2/3
B. 15
C. 20
D. 25
E. 26 2/3
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Cyclist:
60 min = 20 m
5 min = x
x = 5/3
Hiker:
60 min = 4m
5 min = y
y = 1/3
So, during the five min after the cyclist passes the hiker, the cyclist traveled 5/3 mile while the hiker traveled 1/3 mile (because the hiker keeps going after the cyclist passes her.
This means that when the cyclist stops, the hiker has to go 4/3 mile to catch up (5/3 - 1/3).
If she goes 1/3 m in 5 min, then it will take her 20 min to go 4/3 mile (5 min*4).
IMO C.
60 min = 20 m
5 min = x
x = 5/3
Hiker:
60 min = 4m
5 min = y
y = 1/3
So, during the five min after the cyclist passes the hiker, the cyclist traveled 5/3 mile while the hiker traveled 1/3 mile (because the hiker keeps going after the cyclist passes her.
This means that when the cyclist stops, the hiker has to go 4/3 mile to catch up (5/3 - 1/3).
If she goes 1/3 m in 5 min, then it will take her 20 min to go 4/3 mile (5 min*4).
IMO C.
I got the same answer the same way. You need to take into account the distance traveled by the hiker during the 5 minutes the biker uses after he passes the hiker.cammijc wrote:Cyclist:
60 min = 20 m
5 min = x
x = 5/3
Hiker:
60 min = 4m
5 min = y
y = 1/3
So, during the five min after the cyclist passes the hiker, the cyclist traveled 5/3 mile while the hiker traveled 1/3 mile (because the hiker keeps going after the cyclist passes her.
This means that when the cyclist stops, the hiker has to go 4/3 mile to catch up (5/3 - 1/3).
If she goes 1/3 m in 5 min, then it will take her 20 min to go 4/3 mile (5 min*4).
IMO C.
C.
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What you should have done is see that the relative speed of the cyclist is 20 - 14 = 16 mph. 5 minutes elapse after the cyclist passes the hiker, and 5 minutes equals 1/12 of an hour. So 16 X 1/12 = 16/12 = 4/3 miles.Rajani wrote:Hiker - 4m/hr
cyclist - 20 m/hr
Cyclist
-------
60 mins = 20 m
5 mins = x
x = 5/3
So the hiker has to cover 5/3 miles in y mins
60 mins = 4 miles
y mins = 5/3miles
y = 25 mins
4/3 miles is the distance between the cyclist and the hiker when the cyclist decides to stop and wait for the hiker to catch up.
From there, it's a simple d = rt problem. 4/3 = 4t, so t = 1/3 of an hour, 20 minutes.