SOLUTION: A jet plane, flying 110 mph faster than a propeller plane, travels 5280 miles in 4 hours less time than the propeller plane takes to fly the same distance. How fast does each plane

Question 833372: A jet plane, flying 110 mph faster than a propeller plane, travels 5280 miles in 4 hours less time than the propeller plane takes to fly the same distance. How fast does each plane fly?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39614) (Show Source): You can put this solution on YOUR website!
Let r = speed for the propeller plane
Let h = time in hours for propeller plane to go 5280 miles distance

_____________speed_________________time_______________distance
JET__________r+110_________________h-4________________5280
PROP_________r_____________________h__________________5280

JET:
, and since rh=5280 we may substitute,

PROPELLER: rh=5280, and then h=5280/r
Using this, and returning to the JET equation,
-
JET (Returning to):

--
Still, unfinished. Use the general solution to a quadratic equation to solve for r. You can then simply compute r+110 for the jet plane.
Note:
(1) Once getting r, you can also find the time for travel of each plane.
(2) This exercise would be really nicely solved purely in symbolic form, meaning all in variables, not showing specific values. At least a few of this kind or form of exercise has been asked in the past few days on the site.
Answer by MathTherapy(10549) (Show Source): You can put this solution on YOUR website!
A jet plane, flying 110 mph faster than a propeller plane, travels 5280 miles in 4 hours less time than the propeller plane takes to fly the same distance. How fast does each plane fly?

Let propeller plane's speed = S
Then jet plane's speed = S + 110
Propeller plane's time to travel 5,280 miles:
Jet plane's time to travel 5,280 miles:
Since jet plane takes 4 hours less, then we can say that:

5280(S + 110) - 4(S)(S + 110) = 5280S ----- Multiplying by LCD, S(S + 110)

----- Factoring out GCF, 4

(S - 330)(S + 440) = 0
S = 330 OR S = - 440 (ignore)
S, or speed of propeller plane, for 5,280 miles = mph
Speed of jet plane, for 5,280 miles: 330 + 110, or mph
You can do the check!!
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