SOLUTION: To travel 84 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 42 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Find
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Question 728481: To travel 84 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 42 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Find the times and rates of both girls.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = Doreen's time in hrs
= Sue's time in hrs ,
Let = Doreen's speed in mi/hr
= Sue's speed in mi/hr
-------------------------------
Doreen's equation:
(1)
Sue's equation:
(2)
----------------------------
(2)
(1)
Substitute (1) into (2)
(2)
(2)
(2)
Multiply both sides by
(2)
(2)
(2)
Use the quadratic equation
( ignore negative sqrt- can't have negative speed )
and, since
(1)
(1)
(1)
-------------
Sue's time: 4 hrs
Doreen's time: 7 hrs
Sue's speed: 21 mi/hr
Doreen's speed: 6 mi/hr
--------------------
check:
(2)
(2)
(2)
(2)
and
(1)
(1)
(1)
OK
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