Question 153779
Mr. Newton drive to and from work over the same route each day. On Friday, he drives at an average rate of 52 mph/km and is one minute late to work. On Monday, he drives at an average rate of 60 mph/km and is one minute early to work. If he left home at the same time each day, what is the distance Mr. Newton travels one way to work? 
:
First find the times it takes him to get to work, then find the distance from that
:
Let t = time required if he arrives on time (in hrs)
then
(t+{{{1/60}}}) = time if he 1 min late
and
(t-{{{1/60}}}) = time if he 1 min early
;
Write a distance equation: Dist = speed * time
:
Monday dist = Friday dist
60(t-{{{1/60}}}) = 52(t+{{{1/60}}})
:
60t-{{{60/60}}} = 52t+{{{52/60}}} 
:
60t - 52t = {{{60/60}}} + {{{52/60}}}
:
8t = {{{112/60}}} hrs
we can get rid of that denominator (60); convert it to minutes, (mult by 60)
8t = 112
t = {{{112/8}}}
t = 14 minutes for him to arrive on time
:
then we can say
It takes 13 min when he is 1 min early
and 
15 min when he is 1 min late
:
:
Find the distances
52 * {{{15/60}}} = 13 miles
60 * {{{13/60}}} = 13 miles
;
Did this make sense?