SOLUTION: The president of a company traveled 1800 mi by jet and 200 mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took 8 hr. Find the ra

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Question 1148226: The president of a company traveled 1800 mi by jet and 200 mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took 8 hr. Find the rate of the jet
Found 3 solutions by josgarithmetic, josmiceli, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
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              SPEED         TIME         DISTANCE

JET           4r            1800/(4r)             1800

PLANE          r            200/r              200

TOTAL                         8

1800%2F%284r%29%2B200%2Fr=8

450%2Fr%2B200%2Fr=8

650%2Fr=8

8r=650

highlight%284r=325%29, the speed of the jet

Answer by josmiceli(19441) About Me  (Show Source):
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Let +t+ = time in hrs for the jet
+8+-+t+ = time in hrs for the prop plane
Let +s+ = the speed of the prop plane in mi/hr
+4s+ = the speed in mi/hr of the jet
----------------------------------------------------
Equation for jet:
(1) +1800+=+4s%2At+
(1) +450+=+s%2At+
Equation for prop plane:
(2) +200+=+s%2A%28+8+-+t+%29+
-------------------------------
(1) +s+=+450%2Ft+
Plug (1) into (2)
(2) +200+=+%28+450%2Ft+%29%2A%28+8+-+t+%29+
(2) +200t+=+3600+-+450t+
(2) +650t+=+3600+
(2) +t+=+72%2F13+
and
(1) +450+=+s%2At+
(1) +450+=+s%2A%2872%2F13%29+
(1) +s+=+450%2A%2813%2F72%29+
(1) +s+=+4850%2F72+
(1) +s+=+81.25+
and
+4s+=+325+
The speed of the jet is 325 mi/hr
-------------------------------------
check answer:
(1) +1800+=+4s%2At+
(1) +1800+=+325%2A%2872%2F13%29+
(1) +1800+=+1800+
OK
(2) +200+=+s%2A%28+8+-+t+%29+
(2) +200+=+81.25%2A%28+8+-+72%2F13+%29+
(2) +200+=+650+-+450+
(2) +200+=+200+
OK
Get a 2nd opinion if needed

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The president of a company traveled 1800 mi by jet and 200 mi on a prop plane. The rate of the jet was four times the rate of the prop plane. The entire trip took 8 hr. Find the rate of the jet
Let rate of jet be S

Then rate of prop plane = matrix%281%2C3%2C+%281%2F4%29S%2C+or%2C+S%2F4%29

So, we now get the following TIME equation: 

matrix%281%2C3%2C+225%2FS+%2B+100%2FS%2C+%22=%22%2C+1%29 ---- Multiplying by LCN, 8

225 + 100 = S ----- Multiplying by LCD, S

S, or highlight_green%28matrix%281%2C6%2C+Rate%2C+of%2C+jet%2C+%22=%22%2C+325%2C+mph+%29%29