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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1050224: 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(39626) About Me  (Show Source):
You can put this solution on YOUR website!
Essentially the same type of travel rates problem as your other one, but just different values given. EVERYTHING WORKS THE SAME WAY.

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: D%2FT=R 

                  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(52858) About Me  (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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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 = 175%2F20 = 35%2F4 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 175%2F20 = 35%2F4 hours = 8 hours and 45 minutes. The same answer.

Solved.

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


Answer by MathTherapy(10556) About Me  (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.