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

Algebra ->  Rate-of-work-word-problems -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Doreen's time in hrs
+t+-+3+ = Sue's time in hrs ,
Let +s+ = Doreen's speed in mi/hr
+s+%2B+15+ = Sue's speed in mi/hr
-------------------------------
Doreen's equation:
(1) +42+=+s%2At+
Sue's equation:
(2) +84+=+%28+s+%2B+15+%29%2A%28+t+-+3+%29+
----------------------------
(2) +84+=+s%2At+%2B+15t+-+3s+-+45+
(1) +t+=+42%2Fs+
Substitute (1) into (2)
(2) +84+=+s%2A%2842%2Fs%29+%2B+15%2A%2842%2Fs%29+-+3s+-+45+
(2) +84+=+42+%2B+630%2Fs+-+3s+-45+
(2) +87+=+630%2Fs+-+3s+
Multiply both sides by +s+
(2) +87s+=+630+-+3s%5E2+
(2) +3s%5E2+%2B+87s+-+630+=+0+
(2) +s%5E2+%2B+29s+-+210+=+0+
Use the quadratic equation
+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1
+b+=+29+
+c+=+-210+
+s+=+%28-29+%2B-+sqrt%28+29%5E2+-+4%2A1%2A%28-210%29+%29%29%2F%282%2A1%29+
+s+=+%28-29+%2B-+sqrt%28+841+%2B+840%29%29%2F2+
+s+=+%28-29+%2B-+sqrt%28+1681%29%29%2F2+
+s+=+%28-29+%2B+41%29%2F2+ ( ignore negative sqrt- can't have negative speed )
+s+=+12%2F2+
+s+=+6+
+s+%2B+15+=+21+
and, since
(1) +t+=+42%2Fs+
(1) +t+=+42%2F6+
(1) +t+=+7+
+t+-+3+=+4+
-------------
Sue's time: 4 hrs
Doreen's time: 7 hrs
Sue's speed: 21 mi/hr
Doreen's speed: 6 mi/hr
--------------------
check:
(2) +84+=+%28+s+%2B+15+%29%2A%28+t+-+3+%29+
(2) +84+=+%28+6+%2B+15+%29%2A%28+7+-+3+%29+
(2) +84+=+21%2A4+
(2) +84+=+84+
and
(1) +42+=+s%2At+
(1) +42+=+6%2A7+
(1) +42+=+42+
OK