SOLUTION: The Cunninghams are moving across the country. Mr. Cunningham leaves 3.5 hours before Mrs. Cunningham. If he averages 50 mph and she averages 70 mph, how long will it take Mrs. C

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Question 1050225: The Cunninghams are moving across the country. Mr. Cunningham leaves 3.5 hours before Mrs. Cunningham. If he averages 50 mph and she averages 70 mph, how long will it take Mrs. Cunningham to overtake Mr. Cunningham? Solve.
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!
The two travelers catchup problem

h=3.5 hour r=50 mph R=70 mph t, unknown travel time for catchup for traveler at R d, unknown distance upon catchup

BASIC Constant Travel Rate Formula:

SPEED TIME DISTANCE Mr. Cumming r t+h d Mrs. Cumming R t d

Write the equations for the system, and solve for t and d.

Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website!
.
The Cunninghams are moving across the country. Mr. Cunningham leaves 3.5 hours before Mrs. Cunningham.
If he averages 50 mph and she averages 70 mph, how long will it take Mrs. Cunningham to overtake Mr. Cunningham? Solve.
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There are 2 (two) ways to solve the problem

Solution 1

Your governing equation is 50*(t+3.5) = 70*t. (1) The left side is the distance Mr. Cunningham covered from the start to the overtaking point. The right side is the distance Ms. Cunningham covered from the start to the overtaking point. The distances are the same, it gives you the equation (1). "t" is the time counted from Ms. Cunningham start to the overtaking moment. (t+3.5) is the time for Mr. Cunningham on his way. Now simplify and solve the equation (1). 50t + 175 = 70t, or 175 = 70t - 50t, or 20t = 175, or t = = hours = 8 hours and 45 minutes.

Solution 2

After 3.5 hours driving Mr. Cunningham is 3.5*50 = 175 miles ahead. Their relative speed is (70-50) = 20 mph. The time to overtake is = hours = 8 hours and 45 minutes. The same answer.

Solved.

See the lesson
    - Travel and Distance problems
in this site.

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

The Cunninghams are moving across the country. Mr. Cunningham leaves 3.5 hours before Mrs. Cunningham. If he averages 50 mph and she averages 70 mph, how long will it take Mrs. Cunningham to overtake Mr. Cunningham? Solve.

You're asked for time. It is TOTALLY UNNECESSARY and makes absolutely no sense whatsoever to solve for distance, or to find distance.
Therefore, solve for time! If you disagree then feel free to solve for it.