SOLUTION: A private jet flies the same distance in 15 hours that a commercial jet flies in 10 hours. If the speed of the commercial jet was 98mph less than 2 times the speed of the private

Question 1157943: A private jet flies the same distance in 15 hours that a commercial jet flies in 10 hours. If the speed of the commercial jet was 98mph less than 2 times the speed of the private jet, find the speed of each jet.
Found 6 solutions by ikleyn, jim_thompson5910, Alan3354, mananth, greenestamps, MathTherapy:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

From the condition, you have this equation 15*P = 10*(2P - 98) where P is the speed of the Private, and (2P-98) is the speed of the commercial jet. Simplify and solve 15P = 20P - 980 980 = 20P - 15P 5P = 980 P = = 196. ANSWER. Private jet speed is 196 mph; Commercial jet speed is 2*196-98 = 294 mph.

Solved.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Answers:
private jet's speed = 196 mph
commercial jet's speed = 294 mph

===========================================================

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

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A private jet flies the same distance in 15 hours that a commercial jet flies in 10 hours. If the speed of the commercial jet was 98mph less than 2 times the speed of the private jet, find the speed of each jet.
====================
c = commercial jet's speed
p = private jet's speed
---
same distance in 15 hours that a commercial jet flies in 10 hours
----> c = 1.5p
c = 2p - 98
---
1.5p = 2p - 98
-0.5p = -98
p = 196 mi/hr
c = 294 mi/hr
=====================
Not worth a Master's Thesis, IMO.
=========
Slow jets.
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

A private jet flies the same distance in 15 hours that a commercial jet flies in 10 hours. If the speed of the commercial jet was 98mph less than 2 times the speed of the private jet, find the speed of each jet.
the speed of the private jet be x mph
the speed of commercial jet = 2x-98
Distance same=y
y/x=15
y=15x
y/(2x-98)=10
15x/(2x-98)=10
15x = 10(2x-98)
15x = 20x -980
5x=980
x= 196 speed of private jet
speed of commercial jet = 2x-98
2*196-98
392-98= 294 mph speed of commercial jet
CHECK
196*15=2940
294*10 = 2940

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

From the given information, the speed of the private jet is 2/3 the speed of the commercial jet.

Also from the given information, that ratio is x/(2x-98), where x is the speed of the private jet. So

The speeds of the jets are:

private jet: x = 196mph
commercial jet: 2x-98 = 294mph

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
A private jet flies the same distance in 15 hours that a commercial jet flies in 10 hours. If the speed of the commercial jet was 98mph less than 2 times the speed of the private jet, find the speed of each jet.

Let speed of private jet be S
Then speed of commercial jet = 2S - 98
We then get the following DISTANCE equation: 15S = 10(2S - 98)
3S = 2(2S - 98) ------ Factoring out GCF, 5
3S = 4S - 196
3S - 4S = - 196
- S = - 196
Speed of private jet, or
Now, do you think you can find the commercial jet's speed?
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