It takes a plane 40 min longer to fly from Boston to Los Angeles at 525 mi/h than it does to return at 600 mi/h. How far apart are the cities?
a 2,500 miles
b 2,650 miles
c 2,800 miles
d 3,200 miles
2007-11-16 09:05:30 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
D = R * T
Boston to LA
a) D = 525 * T1
LA to Boston
b) D = 600 * T2. Note distance is same.
Compare T1 and T2. One is 40 minutes longer than the other, so T1 = T2 + (40/60), since, notice, time should be in HOURS.
So see this, read the story, or note that, when a plane is flying faster, it takes a SHORTER time, right?
So, the system
a) D = 525 * T1
b) D = 600 * T2 becomes
a) D = 525 * (T2 + 40/60) = 525 * (T2 + 2/3)
b) D = 600 * T2 , equate
525 * (T2 + 2/3) = 600 * T2 , expand
525 *T2 +350 = 600 * T2 , gather
350 = 600 * T2 - 525 *T2 , note signs
350 = 75 T2, div by 75
T2 = 4.666 hours, subs in equation b)
600*4.666 = 2800 miles.
Done.
2007-11-16 09:08:50 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The answer is c) 2800 miles
Let x=time, LA to Boston
Rate is 600mph
Therefore Distance, LA to Boston,=600x
For return trip, time is x+2/3 (2/3 being 40/60 of an hr.)
Rate is 525mph
Therefore Distance, Boston to LA, is (x+2/3)(525)
The distance LA to Boston=distance Boston to LA
Therefore 600x=(x+2/3)(525)
600x=525x+350
600x-525x=350
75x=350
3x=14
x=14/3hrs.
Therefore, since D=Rate X Time
Distance =600x
Distance=600(14/3)
Distance=200 X 14
Distance=2800 miles
2007-11-16 17:29:19 · answer #2 · answered by Grampedo 7 · 0⤊ 0⤋
d= rt
rt = rt
Let x = time at 600 m/h
600x = 525(x + 40/60)
75x = 350
x = 4.6667 hrs
distance = 600x
distance = 2,800 miles
.
2007-11-16 17:19:33 · answer #3 · answered by Robert L 7 · 0⤊ 0⤋
d miles = t*525mi/hr
40 min * 1 hr/60 min = (2/3) hr
d miles = (t-(2/3))* 600mi/hr
= 600t - 400
525t = 600t - 400
75t = 400
t = 5â
hrs
d = 5â
* 525 = 2800 miles
2007-11-16 17:13:04 · answer #4 · answered by DWRead 7 · 0⤊ 0⤋
D?
2007-11-16 17:15:41 · answer #5 · answered by Anonymous · 0⤊ 0⤋