Help with math word problem?

Question

i need help with this word problem:

a plan flies against the wind from center city to new city at a rate of 220mph. on the return trip, the plane flies with the wind at a rate of 250mph. the return trip took one hour less time. how far apart are the two cities?

can you please show your work so i can know how u did it. thanks for your answers!

Answer 1

The formula to be used is

Distance = Speed * Time

Equation 1 -- a plan flies against the wind from center city to new city at a rate of 220mph.

D = 220T

where

D = distance from Center City to New City

T = time plane flew from Center City to New City

Equation 2 -- on the return trip, the plane flies with the wind at a rate of 250mph. the return trip took one hour less time.

D = 250(T - 1)

<< how far apart are the two cities? >>

Since Equation 1 = Equation 2

220T = 250(T - 1)

220T = 250T - 250

250T - 220T = 250

30T = 250

T = 8.33 hours

Since the trip from Center City to New City took 8.33 hours, then the distance between these two cities are

D = 220 * 8.33

D =  1833 miles

Hope this helps.

Answer 2

main equation is time returning = time going - 1 hr.

time is distance over speed, and distance each way is the same.  since the problem asks for distance, we make that the variable:

d/220 - 1 = d/250

250d - 220(250) = 220d

30d = 55000

d = 1833 1/3 mi.

Answer 3

Travel time going (x):

x(220) = (x - 1)(250)

220x = 250x - 250

30x = 250

x = 25/3 or 8 1/3

Distance:

= 220(25/3)

= 5,500/3 or 1,833 1/3

Answer: 1,833 1/3 miles is the distance between two cities.

Proof (distances covered going and returning):

distance going = distance returning

8 1/3 hrs * 220 mph = (8 1/3 - 1 hrs) * 250 mph

25/3 hrs * 220 mph =  7 1/3 hrs * 250 mph

5,500/3 or 1,833 1/3 miles = 22/3 hrs * 250 mph

1,833 1/3 miles = 5,500/3 miles

1,833 1/3 miles = 1,833 1/3 miles