SOLUTION: A man on a motorcycle travels at 45mph down a road. His wife leaves 1 hour later down the same road to bring him his lunch. She is driving the car at 55mph. How long did each of

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Question 1004689: A man on a motorcycle travels at 45mph down a road. His wife leaves 1 hour later down the same road to bring him his lunch. She is driving the car at 55mph. How long did each of them travel?
Found 2 solutions by josmiceli, maxitee:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance each one travels in miles
Let +t+ = the time in hours it takes for the man
to reach the point where his wife catches up
+t+-+1+ = time in hours for wife to catch man
-----------------------------------------
Man's equation:
+d+=+45t+
Wife's equation:
+d+=+55%2A%28+t-1+%29+
-----------------
By susbstitution:
+45t+=+55%2A%28+t-1+%29+
+45t+=+55t+-+55+
+10t+=+55+
+t+=+5.5+
and
+t+-+1+=+4.5+
---------------
The man travels for 5.5 hrs
His wife travels for 4.5 hrs
---------------------
check:
+d+=+45t+
+d+=+45%2A5.5+
+d+=+247.5+
and
+d+=+55%2A%28+t-1+%29+
+d+=+55%2A4.5+
+d+=+247.5+
OK

Answer by maxitee(11) About Me  (Show Source):
You can put this solution on YOUR website!
For the woman, before she left. The man had already covered 45 Miles.
To get our answer, we simply look at how long the speed difference(Between the man and woman) will cover the 45mile gap.
Speed difference between man and woman = 10mph.
Therefore it will take her 45/10 => 4.5hours to meet up with the husband.
In conclusion, the man travelled 5.5hours. While the woman travelled 4.5hours.