SOLUTION: ronald could travel 360 miles in 1/4 time it took Jimmy to travel 480 miles. This was because Ronald's speed exceeded that of Jimmy by 60 mph. What ere the speeds and times of bo

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Question 771266: ronald could travel 360 miles in 1/4 time it took Jimmy to travel 480 miles. This was because Ronald's speed exceeded that of Jimmy by 60 mph. What ere the speeds and times of both?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Jimmy's time in hrs to travel 480 mi
+t%2F4+ = Ronald's time to travel 360 mi
Let +s+ = Jimmy's speed in mi/hr
+s+%2B+60+ = Ronald's speed in mi/hr
---------------------------------
Jimmy's equation:
(1) +480+=+s%2At+
Ronald's equation:
(2) +360+=+%28+s+%2B+60+%29%2A%28+t%2F4+%29+
---------------------------
(2) +360+=+%28+s%2At+%29%2F4+%2B+15t+
(2) +360+=+t%2A%28+s%2F4+%2B+15+%29+
and
(1) +t+=+480%2Fs+
Substitute (1) into (2)
(2) +360+=+%28+480%2Fs+%29%2A%28+s%2F4+%2B+15+%29+
(2) +360+=+480%2F4+%2B+%28+480%2A15+%29%2F+s+%29+
(2) +360+=+120+%2B+7200%2Fs+
(2) +240+=+7200%2Fs+
(2) +s+=+7200%2F240+
(2) +s+=+30+
+s+%2B+60+=+90+
and
(1) +480+=+s%2At+
(1) +480+=+30%2At+
(1) +t+=+16+
+t%2F4+=+4+
Jimmy's speed is 30 mi/hr
His time is 16 hrs
Ronald's speed is 90 mi/hr
His time is 4 hrs
--------------
check:
(2) +360+=+%28+s+%2B+60+%29%2A%28+t%2F4+%29+
(2) +360+=+%28+30+%2B+60+%29%2A%28+16%2F4+%29+
(2) +360+=+90%2A4+
(2) +360+=+360+
OK