SOLUTION: John covered a total distance of 16 km by walking for 45 min and running for 40 min. the next day he covered the same distance by walking for 30 min and running for 48 min How fas

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Question 498236: John covered a total distance of 16 km by walking for 45 min and running for 40 min. the next day he covered the same distance by walking for 30 min and running for 48 min How fast does he walk and how fast does he run assuming these rates are constant.
D1=D2=16 km
R1=walking
r2=running
r1T1=R2T2
3/4R1+2/3R2=16km
1/2R1+4/5R2=16km
3/4R1+2/3R2=1/2R1+4/5R2
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +%283%2F4%29%2Ar%5B1%5D+%2B+%282%2F3%29%2Ar%5B2%5D+=+16+
(2) +%281%2F2%29%2Ar%5B1%5D+%2B+%284%2F5%29%2Ar%5B2%5D+=+16+
Multiply both sides of (1) by 12
Multiply both sides of (2) by 10
(1) +9r%5B1%5D+%2B+8r%5B2%5D+=+192+
(2) +5r%5B1%5D+%2B+8r%5B2%5D+=+160+
Subtract (2) from (1)
(1) +9r%5B1%5D+%2B+8r%5B2%5D+=+192+
(2) +-5r%5B1%5D+-+8r%5B2%5D+=+-160+
+4r%5B1%5D+=+32+
+r%5B1%5D+=+8+ km/hr
Plug this result back into (2)
(2) +5%2A8+%2B+8r%5B2%5D+=+160+
(2) +40+%2B+8r%5B2%5D+=+160+
(2) +8r%5B2%5D+=+120+
(2) +r%5B2%5D+=+15+ km/hr
He walks at 8 km/hr
He runs at 15 km/hr