Question 1157943
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Answers:
private jet's speed = <font color=red size=4>196 mph</font>
commercial jet's speed = <font color=red size=4>294 mph</font>


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Work Shown:


p = speed of private jet
c = speed of commercial jet
speeds are in mph


" the speed of the commercial jet was 98mph less than 2 times the speed of the private jet"
So,
c = 2p-98


The private jet travels some distance d miles in t = 15 hours
distance = rate*time
d = r*t
d = p*15
d = 15p



and the commercial jet travels that same distance in t = 10 hours
d = r*t
d = c*10
d = 10c


We're referring to the same distance d value, so we can equate the two right hand sides of the equations above
15p = 10c


Now plug in c = 2p-98
15p = 10c
15p = 10( c )
15p = 10( 2p-98 ) ... c has been replaced with 2p-98
15p = 20p - 980 .... distribute
15p-20p = -980 .... subtract 20p from both sides
-5p = -980
p = -980/(-5) .... divide both sides by -5
p = 196


Use this value of p to find the value of c
c = 2p - 98
c = 2*196 - 98 ... replace p with 196
c = 392 - 98
c = 294


In summary, we found:
p = 196
c = 294
meaning the private jet travels a speed of 196 mph and the commercial jet travels a speed of 294 mph

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