SOLUTION: A company president flew 1110 miles in a corporate jet but returned in a smaller plane that could fly only half as fast. If the total travel time was 9 hours, find the speeds of th

Question 1166630: A company president flew 1110 miles in a corporate jet but returned in a smaller plane that could fly only half as fast. If the total travel time was 9 hours, find the speeds of the planes.
corporate jet
mph
smaller plane
mph

Found 3 solutions by Boreal, josgarithmetic, greenestamps:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
x hours going
9-x hours returning
time to go 1110 miles is 1110/s1, where s1 is speed of jet
time to go 1110 miles is 1110/s2, where s2 is speed of jet
so x=1110/s1
9-x=1110/s2
1110=s1x
1110=s2(9-x)
therefore, s1x=s2(9-x)
but s1=2s2
so 2s2x=s2(9-x)
and 2x=9-x
and 3x=9
so x=3 hours going there with speed 1110/3=370 mph in jet
and 6 hours returning at 1110 miles or 185 mph in smaller plane.
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
------------------------------------------------------
..., flew 1110 miles in a corporate jet but returned in a smaller plane that could fly only half as fast. If the total travel time was 9 hours, find the speeds of the planes.
-----------------------------------------------------

r, speed of small plane
2r, speed of jet
d = 1110 miles
t = 9 hours total

SPEED TIME DISTANCE Jet 2r d/(2r) d Plane r d/r d TOTAL t

Solve this time sum equation for r:

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Solve most of the problem using common sense instead of formal algebra: Flying half as fast means the trip takes twice as long.

Since the total time was 9 hours, that means 3 hours at the higher speed and 6 hours at the lower speed.

ANSWERS:
corporate jet speed: 1110/3 = 370 mph
smaller plane speed: half of 370 mph = 185 mph

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