SOLUTION: Dave and sara live 50 miles apart and travel towards each other on their bikes. Sara leaves on time and dave leaves 2 hours later but tries to make up for it by riding 7 mph faster

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Question 581312: Dave and sara live 50 miles apart and travel towards each other on their bikes. Sara leaves on time and dave leaves 2 hours later but tries to make up for it by riding 7 mph faster than sara.Find the speed of both sara and dave on their bikes, if sara is on the bike for 4 hours.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Sarah's speed in mi/hr
+s+%2B+7+ = Dave's speed in mi/hr
given:
Sarah gets a head start of +d+=+2s+
They are +50+-+2s+ miles apart when Dave leaves
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Now I can think of Sarah as standing still and
Dave moving towards her at the sum of their speeds
If Sarah is on her bike for +4+ hrs, then
when Dave starts, they both travel for +2+ more hrs
+50+-+2s+=+%28+s+%2B+s+%2B+7+%29%2A2+
+50+-+2s+=+%28+2s+%2B+7+%29%2A2+
+50+-+2s+=+4s+%2B+14+
+6s+=+36+
+s+=+6+
+s+%2B+7+=+13+
Sarah's speed is 6 mi/hr
Dave's speed is 13 mi/hr
check:
Their separate distances are:
Dave:
+%28+s+%2B+7%29%2A2+=+13%2A2%0D%0A%7B%7B%7B+13%2A2+=+26+ mi
Sarah:
+2s+%2B+s%2A2+=+4s+
+4s+=+4%2A6+
+4%2A6+=+24+ mi
and
+24+%2B+26+=+50+ mi
OK