I Need Help with a really hard math problem............?

Question

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?

Answer 1

Heh okey then

THe answer is 2800, that is the places are separated by a distance of 2800

Assume the distance to be x,

In the first case, where the plane travels at 525 mph,

x/525= t (assuming t to be the time taken) --------------- I

In the second case, where the plane travels at 600moh,

x/600 = t - 40/60 [I am subtracting 40/60 because this takes 40 minutes lesser, and since the units are in hours, i have to convert 40 minutes to hours that is 40/60 or 2/3)

Therefore...

x/600 = t - 2/3 ------------------ II

Subtracting II - I, we get...

x/600 - x/525 = -2/3 [we primarily subract them in order to eliminate the t variable which doesnt serve much use from here on]

Solving the equation,

we get, (525x-600x) / (525*600) = -2/3 [taking lcm...]

Finally we get the answer as
x = 2800 :)

Answer 2

40 x = 600-525
= 75
40x75=3000
x=3000 Miles apart

Answer 3

formulate the equation. Let t (in hours) be the time taken to fly from Los Angeles to Boston, we have

distance = 525(t + 40/60) = 600t. Solve for t, then find
the distance.

Answer 4

D (distance) = 600T (time)
D = 525 (T + 40)

So 525 (T+40) = 600T, or 525T + 21,000 = 600T.
Subtract 525T from both sides to get 21,000 = 75T

So it takes 280 minutes to fly between the cities at 600mph, so the cities are 4.666 * 600 = ~2800 mi apart.
(We had to convert 280 min to 4.666 hours since the speed is in miles per HOUR.)

Checking we get 525 (4.666 + .6666) = ~2800mi, so we are correct.

Answer 5

assume it takes t hours to fly at 600mph

so the distance=600t miles

at the slower speed it takes t+2/3 hours

so the distance=525(t+2/3)

hence 600t=525t+525*2/3

or 75t=350

so dist = 600t=600*350/75=8*350=2800 miles

Answer 6

Distance = Speed * Time
Distance from Boston to LA if speed is 600mi/h= 600mi/h * x hour = 600x mi
Distance from Boston to LA if speed is 525mi/h = 525mi/h * (40+x)
= 525 * (40/60 hour + x )
= 175 * 525x
to count x=
=175*535x = 600x
= 600x-525x = 175
= 75x = 175
x =2.34 hours (2 decimal place)

distance = 600 * 2.34 =1400mi

Answer 7

2800 miles apart