SOLUTION: abu ran for 1/3 of an hour and then walked for half an hour at the rate of 3km/h. in all, he had covered 4 km. how fast did he run?

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Question 253133: abu ran for 1/3 of an hour and then walked for half an hour at the rate of 3km/h. in all, he had covered 4 km. how fast did he run?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write 2 equations,1 for running
and 1 for walking
d%5Br%5D+=+r%5Br%5D%2At%5Br%5D
and
d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D
given:
t%5Br%5D+=+1%2F3 hr
t%5Bw%5D+=+1%2F2 hr
r%5Bw%5D+=+3 km/hr
d%5Br%5D+%2B+d%5Bw%5D+=+4 km
-----------------
d%5Br%5D+=+r%5Br%5D%2At%5Br%5D
d%5Br%5D+=r%5Br%5D%2A%281%2F3%29
and
4+-+d%5Br%5D+=+3%2A%281%2F2%29
-d%5Br%5D+=+3%2F2+-+4
-d%5Br%5D+=+-5%2F2
d%5Br%5D+=+5%2F2
and, since
d%5Br%5D+=r%5Br%5D%2A%281%2F3%29
5%2F2+=+r%5Br%5D%2A%281%2F3%29
r%5Br%5D+=+15%2F2
He ran 7.5 km/hr
check:
d%5Br%5D+=+r%5Br%5D%2At%5Br%5D
5%2F2+=+%2815%2F2%29%2A%281%2F3%29
5%2F2+=+5%2F2
OK