SOLUTION: Two planes make a 1680 mile flight, one flying 10 miles per hour faster than the other. The quicker plane makes the trip 4 hours faster. How long did it take the slower plane to co

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Question 1086475: Two planes make a 1680 mile flight, one flying 10 miles per hour faster than the other. The quicker plane makes the trip 4 hours faster. How long did it take the slower plane to complete the flight?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
                 SPEED     TIME          DISTANCE
Fast Plane       r+10     1680/(r+10)     1680
Slow Plan         r       1680/r          1680
Difference                 4

1680%2Fr-1680%2F%28r%2B10%29=4
-
420%2Fr-420%2F%28r%2B10%29=1
420%28r%2B10%29-420r=r%5E2%2B10r
420r%2B4200-420r=r%5E2%2B10r
4200=r%5E2%2B10r
r%5E2%2B10r-4200=0

discrim, 100%2B4%2A4200=16900=10%5E2%2A13%5E2=130%5E2

r=%28-10%2B130%29%2F2
highlight_green%28r=60%29


Slower Plane: 1680%2F60=highlight%2828%29, hours

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

Two planes make a 1680 mile flight, one flying 10 miles per hour faster than the other. The quicker plane makes the trip 4 hours faster. How long did it take the slower plane to complete the flight?
Let time slower plane takes be T

Then time faster plane takes = T – 4

We then get the following SPEED equation: matrix%281%2C3%2C+%221%2C680%22%2FT%2C+%22=%22%2C+%221%2C680%22%2F%28T+-+4%29+-+10%29

Solve this to get a time of highlight_green%28matrix%281%2C2%2C+28%2C+hours%29%29 for the slower plane.