SOLUTION: John travels by train to go home and arrives at the railway station every day at 17h00. His wife travels by car to pick him up at the station and arrives at the station at precise

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Question 378772: John travels by train to go home and arrives at the railway station every day at 17h00. His wife travels by car to pick him up at the station and arrives at the station at precisely 17h00. One day John took an earlier train and arrived at the station at 16h00 and was unable to phone his wife. He then started walking home hoping to meet his wife who would be on her way to pick him up. She did pick him up and they arrived home 12 min earlier than normal.
a) Assuming the wife travels at 60km per hour, how far did John walk?
b) How far is their home from the station?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
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Let John walk for w km in 1 hour.
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The wife in 1 hour travels 60 km.
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The distance to station is 60+w km.
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time taken to & fro =t
Everyday the time taken for them = 2(60+w)/60 =t................1
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Today she drove for 1 hour
so she drove 60 km.
to day they reached 12 minutes early. = 1/5 hour
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today distance traveled = 120
speed = 60 km/h
time = 120/60 = t-1/5
2= t -1/5
multiply by 5
10= 5t -1
5t=11
/5
t = 11/5
plug this value in equation 1
2(60+w)/60 =t
2(60+w)/60 =11/5
multiply by 5
2(60+w)*5/60 = 11*5/5
2(60+w)/12= 11
2(60+w)=132
60+w= 132/2
60+w=66
-60
w= 66-60
w= 6 .. John walked for 6 km.
distance to station = 60+6 = 66 km.
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m.ananth@hotmail.ca