Question

With a certain tail wind a jet aircraft arrives at its destination, 1,890 miles away, in 3 hours. Flying against the same wind, the plane makes the return trip in 3 3/8 hours. Find the wind speed and the plane's airspeed. plz help!!

Answer 1

Variables:
d = distance
r = rate
t = time
c = speed of current

Given: 1,890 miles away
Means: d = 1890

Given: trip with tail wind take 3 hours
Means: t_tailwind = 3

Given: Flying against the same wind, the plane makes the return trip in 3 3/8 hours
Means: t_headwind = 3 3/8

Convert 3 3/8 hours to a decimal.
3 3/8 hours =
3 hours + 3/8 hours =
3 hours + 0.375 hours =
3.375 hours

HINT: Write what you know in a table.

..................... distance ....... rate ...... time
head wind ...... 1890 ........... r - w ...… 3.375
tail wind …...... 1890 ........... r + w ..… 3
total ............... 3780 ........... ---- ........ 6.375

Remember that the distance formula is d = r * t. Apply this to the table.

...................... distance ................... rate ...... time
head wind ...... 1890 = 3.375(r - w) .... r - w ..… 3.375
tail wind …...... 1890 = 3(r + w) ......... r + w .… 3
total ............... 3780 ....................... ---- ........ 6.375

You have 2 equations to use.
1890 = 3.375(r - w)
1890 = 3(r + w)

Solve the first one for r.
1890 = 3.375(r - w)
1890 = 3.375(r) + 3.375(-w)
1890 = 3.375r - 3.375w
1890 + 3.375w = 3.375r
(1890 + 3.375w) / 3.375 = 3.375r / 3.375
(1890 / 3.375) + (3.375w / 3.375) = r
560 + w = r

Plug this into the second equation.
1890 = 3(r + w)
1890 = 3(560 + w + w)
1890 = 3(560 + 2w)
1890 = 3(560) + 3(2w)
1890 = 1680 + 6w
1890 - 1680 = 6w
1890 - 1680 = 6w
210 = 6w
210 / 6 = 6w / 6
35 = w

Plug this into 560 + w = r to find r.
560 + w = r
560 + 35 = r
595 = r

ANSWER: The wind speed is 35 mph; the plane's airspeed is 595 mph.

CHECK:
...................... distance ....................... rate ............ time
head wind ...... 1890 = 3.375(595 - 35) .... 595 - 35 ..… 3.375
tail wind …...... 1890 = 3(595 + 35) ......... 595 + 35 .… 3
total ............... 3780 ............................. ---- ............. 6.375

...................... distance .............. rate ..... time
head wind ...... 1890 = 1890 ......... 560 ..… 3.375
tail wind …...... 1890 = 1890 ......... 630 .… 3
total ............... 3780 .................... ---- ..... 6.375

Answer 2

good job, but it would be nice if you give the poster a chance to reply , ie, dont give the complete answer

Answer 3

okay next time i will do that

Answer 4

@cierra.whisper thank you cierra