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Question 291181: Sheri drove southeast from Albuquerque to Roswell and then south to Carlsbad. She average 75 mph along the route from Albuquerque to Roswell and averaged 70 mph from Roswell to Carlsbad. She covered the entire 220 miles in 3 hours. How long did she take to drive from Albuquerque to Roswell?
A) 2 hours
B) 1 Hour
C) 1.5 hours
d) 2.5 hours
Answer by Grinnell(63)   (Show Source):
You can put this solution on YOUR website! Again RATE (SPEED) X TIME = DISTANCE
IN THIS PROBLEM WE ARE ADDING TWO DIFFERENT TIMES TO TOTAL THREE HOURS.
STOPP!! UNDERSTAND THIS CONCEPT HERE--ONE TIME PLUS ANOTHER TIME ADDS UP TO THREE HOURS.
NOW IN THE FORMULA ABOVE WE REPRESENT TIME BY DISTANCE OVER SPEED.
SO, THE D/S (TIME IT TAKES TO TRAVEL FROM ALB. TO ROS.) + D/S (TIME IT TAKES TO TRAVEL FROM ROS. TO CARL.) =3 HOURS.
NOW TOTAL DISTANCE IS 220 MILES. SO LET 220-X/75 BE THE TIME IT TAKES TO DRIVE TO ROS.
LET X/70 BE THE TIME IT TAKES TO DRIVE TO CARL.
THEN WE HAVE 3 HOURS = 220-X/75 + X/70
MULTIPLY THRU BY (75)(70) TO REMOVE THE DENOMINATOR--REVIEW ADDING FRACTIONS IF NEED BE HERE.
WE GET 15,750=15,400 -70X + 75X
350=5X
70=X
WE SUBSTITUTE BACK INTO 220-X/75, WE GET 150/75=2HOURS A) IS THE ANSWER
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