SOLUTION: A takes one hour to run a certain distance. B takes 40 minutes to run the same distance. One day A started his running at 4 p.m and B started his running 10 minutes later. What is

Algebra ->  Test -> SOLUTION: A takes one hour to run a certain distance. B takes 40 minutes to run the same distance. One day A started his running at 4 p.m and B started his running 10 minutes later. What is       Log On


   

Question 1068653: A takes one hour to run a certain distance. B takes 40 minutes to run the same distance. One day A started his running at 4 p.m and B started his running 10 minutes later. What is the time when B passes A? (explain the method plz)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate x Time = Distance
.
.
.
Find A's rate in terms of B's rate,
A ran a distance in 1 hour(60 minutes),
R%5BA%5D%2860%29=D
B ran the same distance in 40 minutes.
R%5BB%5D%2840%29=D
So,
60R%5BA%5D=40R%5BB%5D
R%5BA%5D=%282%2F3%29R%5BB%5D
So on the one day, find the time when A's distance equals B's distance (remember A has a 10 minute head start so we'll count the time 0 when B starts)
R%5BA%5D%2A%28t%2B10%29=D
R%5BB%5D%2At=D
R%5BA%5D%28t%2B10%29=R%5BB%5D%2At
Now substitute from above,
%282%2F3%29R%5BB%5D%28t%2B10%29=R%5BB%5D%2At
%282%2F3%29%28t%2B10%29=t
2%28t%2B10%29=3t
2t%2B20=3t
t=20min
So it's 20 minutes after B started running, 4:10+0:20=4:30.