SOLUTION: Brandy dawson and Jason dodge start a motorcycle trip at the same point north of Fort Worth, Texas. Both traveling to San Antonio, Texas, a distance of about 400 kilometers. Brandy

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Question 1042463: Brandy dawson and Jason dodge start a motorcycle trip at the same point north of Fort Worth, Texas. Both traveling to San Antonio, Texas, a distance of about 400 kilometers. Brandy rides 30 kilometers per hour faster than Jason does. When Brandy reaches her destination, Jason has only traveled to Austin, Texas, a distance of about 250 kilometers. Determine the approximate speed of each motorcycle.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for both of them
Let +s+ = Jason's speed in km/hr
+s+%2B+30+ = Brandy's speed in km/hr
Jason's equation:
(1) +250+=+s%2At+
Brandy's equation:
(2) +400+=+%28+s+%2B+30+%29%2At+
---------------------
(1) +t+=+250%2Fs+
Substitute (1) into (2)
(2) +400+=+%28+s+%2B+30+%29%2A%28+250%2Fs+%29+
(2) +400s+=+250s+%2B+7500+
(2) +150s+=+7500+
(2) +15s+=+750+
(2) +s+=+50+
and
+s+%2B+30+=+80+
-------------------
Brandy's speed was 80 km/hr
Jason's speed was 50 km/hr
--------------------------
check:
(1) +t+=+250%2Fs+
(1) +t+=+250%2F50+
(1) +t+=+5+ hrs
and
(2) +400+=+%28+s+%2B+30+%29%2At+
(2) +400+=+%28+50+%2B+30+%29%2At+
(2) +400+=+80t+
(2) +t+=+400%2F80+
(2) +t+=+5+ hrs
OK