SOLUTION: A plane can fly 1315km in 70 minutes with the wind. Flying against the wind,the plane travels the same distance in 65minutes. Find the speed of the wind and the speed of the plane

Question 825259: A plane can fly 1315km in 70 minutes with the wind. Flying against the wind,the plane travels the same distance in 65minutes. Find the speed of the wind and the speed of the plane in still air.

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
---
x = airplane speed
y = wind speed
---
s = d / t
---
x + y = 1315/(70/60)
x - y = 1315/(65/60)
---
put the system of linear equations into standard form
---
x + y = 1127.142857142857110
x - y = 1213.846153846154039
---
copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution:
x = airplane speed = 1170.4945 kph
y = wind speed = -43.351648 kph
---
NOTE:
the negative wind speed indicates that there is an error in the problem statement.
the error is obvious: an airplane cannot fly a fixed distance AGAINST the wind in LESS time than it takes to fly the same distance WITH the wind, assuming that the airplane's airspeed is the same during both the upwind and downwind segments of the flight.
---
system matrix
1 1
1 -1
---
inverse of system matrix
0.5 0.5
0.5 -0.5
---
determinant of system matrix = -2
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 4-equations 4-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
RELATED QUESTIONS
Flying with the wind, a plane can fly 800 miles in 2 hours. Against the wind the plane... (answered by Alan3354)

A light private plane can fly 120 mph in still air. Flying against the wind, the plane... (answered by checkley77)

A plane can fly 180 mph in calm air. Flying with the wind, the plane can fly 600 mi in... (answered by lwsshak3)

A plane can fly 190 mph in calm air. Flying with the wind, the plane can fly 836 mi in... (answered by ewatrrr,Theo)

Flying with the wind, a plane flew 960 mi in 4 h. Against the wind, the plane required 6... (answered by Alan3354)

Flying with the wind, a plane flew 800 mi in 4 h. Against the wind, the plane required 8... (answered by Alan3354)

Flying with the wind, a plane flew 1500 mi in 5 h. Against the wind, the plane required 6 (answered by richwmiller)

Flying with the wind, a plane flew 1200 mi in 4h. Against the wind, the plane required 5h (answered by josgarithmetic)

Flying with the wind, a plane flew 960 mi in 3 h. Against the wind, the plane required 4... (answered by lwsshak3)