SOLUTION: To travel 60 miles, it takes Sue, riding a moped, 2 hours8 less time than it takes Doreen to travel 50 miles riding a bicycle. Sue travels 10 miles per hour faster than Doreen.

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: To travel 60 miles, it takes Sue, riding a moped, 2 hours8 less time than it takes Doreen to travel 50 miles riding a bicycle. Sue travels 10 miles per hour faster than Doreen.       Log On

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Question 1031959: To travel 60 miles, it takes Sue, riding a moped, 2 hours8
less time than it takes Doreen to travel 50 miles riding a
bicycle. Sue travels 10 miles per hour faster than Doreen.
Find the times and rates of both girls.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Doreen's speed in mi/hr
+s+%2B+10+ = Sue's speed in mi/hr
Let +t+ = Doreen's time in hrs to travel 50 mi
riding bicycle
+t+-+2+ = Sue's time in hrs to travel 60 mi
------------------------
Equation for Doreen:
(1) +50+=+s%2At+
Equation for Sue:
(2) +60+=+%28+s%2B10+%29%2A%28+t+-+2+%29+
---------------------------
(1) +s+=+50%2Ft+
Plug this into (2)
(2) +60+=+%28+50%2Ft+%2B10+%29%2A%28+t+-+2+%29+
(2) +60+=+50+%2B+10t+-+100%2Ft+-+20+
(2) +30+=+10t+-+100%2Ft+
(2) +30t+=+10t%5E2+-+100+
(2) +10t%5E2+-+30t+-+100+=+0+
(2) +t%5E2+-+3t+-+10+=+0+
(2) +%28+t+-+5+%29%2A%28+t+%2B+2+%29+=+0+ ( by looking at it )
+t+=+5+ ( time must be positive )
and
+t+-+2+=+3+
---------------
(1) +50+=+s%2A5+
(1) +s+=+50%2F5+
(1) +s+=+10+
and
+s%2B+10+=+20+
------------------
Doreen's speed = 10 mi/hr
Doreen's time = 5 hrs
Sue's speed = 20 mi/hr
Sue's time = 3 hrs
------------------------
check answers:
(1) +50+=+s%2At+
(1) +50+=+10%2A5+
(1) +50+=+50+
and
(2) +60+=+%28+s%2B10+%29%2A%28+t+-+2+%29+
(2) +60+=+20%2A3+
(2) +60+=+60+
OK