SOLUTION: a plane traveled "2835" miles with the wind in 4.5 hours and "2475" miles against the wind in the same amount of time. find the speed of the wind.
Question 1171013: a plane traveled "2835" miles with the wind in 4.5 hours and "2475" miles against the wind in the same amount of time. find the speed of the wind. Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source): You can put this solution on YOUR website! rate * time = distance.
with the wind, the rate is additive.
let p equal the rate of the plane and w equal the rate of the wind.
the combined rate is (p + w).
against the wind, the rate is subtractive.
let p equal the rate of the plane and w equal the rate of the wind.
the combined rate is (p - w).
with the wind, the plane traveled 2835. miles in 4.5 hours.
the formula for that is:
(p + w) * 4.5 = 2835.
against the wind, the place traveled 2475 miles in the same amount of time.
the formula for that is:
(p - w) * 4.5 = 2475.
you have two equations that need to be solved simultaneously.
they are:
(p + w) * 4.5 = 2835.
(p - w) * 4.5 = 2475.
simplify these equations to get:
4.5 * p + 4.5 * w = 2835.
4.5 * p - 4.5 * w = 2475
add these two equations together to get:|
9 * p = 5310
solve for p to get:
p = 5310 / 9 = 590
that's the speed of the plane.
go back to the two equations that need to be solved simultaneously and replace p with 590 to get:
(p + w) * 4.5 = 2835 becomes (590 + w) * 4.5 = 2835
(p - w) * 4.5 = 2475 becomes (590 - w) * 4.5 = 2475
simplify to get:
4.5 * 590 + 4.5 * w = 2835
4.5 * 590 - 4.5 * w = 2475.
in the first of these equations, simplify and solve for w to get:
w = (2835 - 2655) / 4.5 = 40
in the second of these equations, simplify and solve for w to get:
w = (2475 - 2655) / -4.5 = 40
looks like the speed of the wind is 40 miles per hour and the speed of the plane is 590 miles per hour.
replace p and w with those values in the original equations to get:
(p + w) * 4.5 = 2835 becomes (590 + 40) * 4.5 = 2835 which becomes 630 * 4.5 = 2835 which becomes 2835 = 2835 which is true.
(p - w) * 4.5 = 2475 becomes (590 - 40) * 4.5 = 2475 which becomes 550 * 4.5 = 2475 which becomes 2475 = 2475 which is true.
your solution is that the speed of the wind is 40 miles per hour.
this solution has been confirmed to be good.
Let speeds, of plane in still air, and wind, be S and W, respectively
We then get:
Also,
630 - W - W = 550 ------ Substituting 630 - W for S in eq (ii)
- 2W = 550 - 630
- 2W = - 80
Wind speed, or