SOLUTION: Melanie left NYC travelling 78 mph. Nancy, to catch up, left some time later driving at 87 mph. Nancy caught up after 5 hours. How long was Melanie driving before Nancy caught u

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Question 1125733: Melanie left NYC travelling 78 mph. Nancy, to catch up, left some time later
driving at 87 mph. Nancy caught up after 5 hours. How long was
Melanie driving before Nancy caught up?
Found 3 solutions by josgarithmetic, josmiceli, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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Let x be Melanie's travel time from beginning until Nancy catchup.

cross%2878x=87%285-x%29%29
cross%2878x=87%2A5-87x%29
cross%28%2878%2B87%29x=87%2A5%29
cross%28highlight_green%28x=2.636%29%2Ahours%29

2 hours 38 minutes, Melanie's travel time.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d%5B1%5D+ = Melanie痴 head start in miles
+87%2A5+=+435+ = distance Nancy travels
Until she catches up with Melanie
覧覧覧覧覧-
Melanie痴 equation:
(1) +435+-+d%5B1%5D+=+78%2A5+
(1) +d%5B1%5D+=+435+-+390+
(1) +d%5B1%5D+=+45+
Melanie痴 time to travel +d%5B1%5D+ is:
+t%5B1%5D+=+d%5B1%5D+%2F+78+
+t%5B1%5D+=+45%2F78+
+t%5B1%5D+=+.577+ hrs
覧覧覧覧覧
Check the math

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
From the start till the catching up moment Nancy traveled  5*87 = 435 miles.


Melanie traveled the same distance, and her way consisted of two parts:

    a) head -start distance, and
 
    b)  5*78 = 390 miles.


Hence, Melanie's head-start was  435 - 390 = 45 miles.


To cover this distance of 45 miles, Melanie took  45%2F78 = 15%2F26 of an hour =~ 0.5769 of an hour =~ 34.6 minutes.

Solved.

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The solution by  @josmiceli  is correct.

The solution by  @josgarithmetic  is   T O T A L L Y   W R O N G.