SOLUTION: an engineer traveled 165 miles by car and then an additional 660 miles by plane. the rate of the plane was four times the rate of the car. the total trip took 6 hours. find the rat

Algebra ->  Rate-of-work-word-problems -> SOLUTION: an engineer traveled 165 miles by car and then an additional 660 miles by plane. the rate of the plane was four times the rate of the car. the total trip took 6 hours. find the rat      Log On


   

Question 750421: an engineer traveled 165 miles by car and then an additional 660 miles by plane. the rate of the plane was four times the rate of the car. the total trip took 6 hours. find the rate of the car and plane.
the only thing i could think of was the distance formula but got stumped there.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r%5Bc%5D+ = the rate of the car in mi/hr
Let +r%5Bp%5D+ = the rate of the plane in mi/hr
Let +t%5Bc%5D+ = the time in hrs for the car
Let +t%5Bp%5D+ = the time in hrs for the plane
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given:
(1) +r%5Bp%5D+=+4r%5Bc%5D+
(2) +t%5Bc%5D+%2B+t%5Bp%5D+=+6+
(3) +165+=+r%5Bc%5D%2At%5Bc%5D+
(4) +660+=+r%5Bp%5D%2At%5Bp%5D+
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There are 4 equations and 4 unknowns, so it's solvable
(3) +t%5Bc%5D+=+165+%2F+r%5Bc%5D+
(4) +t%5Bp%5D+=+660+%2F+r%5Bp%5D+
Substitute these results into (2)
(2) +165%2F+r%5Bc%5D+%2B+660+%2F+r%5Bp%5D+=+6+
Multiply both sides by +r%5Bc%5D%2Ar%5Bp%5D+
(2) +165r%5Bp%5D+%2B+660r%5Bc%5D+=+6%2Ar%5Bc%5D%2Ar%5Bp%5D+
Divide both sides by 3
(2) +55r%5Bp%5D+%2B+220r%5Bc%5D+=+2%2Ar%5Bc%5D%2Ar%5Bp%5D+
Substitute (1) into (2)
(2) +55%2A4r%5Bc%5D+%2B+220r%5Bc%5D+=+2%2Ar%5Bc%5D%2A4r%5Bc%5D+
(2) +220r%5Bc%5D+%2B+220r%5Bc%5D+=+8%2A%28+r%5Bc%5D+%29%5E2+
(2) +8%2A%28+r%5Bc%5D+%29%5E2+=+440r%5Bc%5D+
(2) +r%5Bc%5D%2A%28+8%2Ar%5Bc%5D+-+440+%29+=+0+
+r%5Bc%5D+=+55+
and, since
(1) +r%5Bp%5D+=+4r%5Bc%5D+
(1) +r%5Bp%5D+=+220+
The rate of the car is 55 mi/hr
The rate of the plane is 220 mi/hr
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check:
(3) +165+=+r%5Bc%5D%2At%5Bc%5D+
(3) +165+=+55%2At%5Bc%5D+
(3) +t%5Bc%5D+=+3+ hrs
and
(4) +660+=+r%5Bp%5D%2At%5Bp%5D+
(4) +660+=+220%5D%2At%5Bp%5D+
(4) +t%5Bp%5D+=+3+ hrs
and
(2) +t%5Bc%5D+%2B+t%5Bp%5D+=+6+
(2) +3+%2B+3++=+6+
OK