a plane flying with the tail wind flew 600 miles in 5hrs Aga

a plane flying with the tail wind flew 600 miles in 5hrs. Against the wind, the plane requires 6 hours to fly the same distance. Find the rate of the plane in the calm air and the rate of the wind?

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate of plane in calm air
And let w=rate of the wind
Now we are told the following: (t=d/r)
5=600/(r+w) Multiply each term by (r+w)
5(r+w)=600 get rid of parens (distributive law)
5r+5w=600 divide each term by 5
r+w=120------------------------------------------------eq1
and
6=600/(r-w)Multiply each term by (r-w)
6(r-w)=600 get rid of parens
6r-6w=600 divide each term by 6
r-w=100-------------------------------------eq2
(NOTE: WHEN TRAVELLING WITH THE WIND, WE HAVE TO ADD THE WIND SPEED AND AGAINST THE WIND, WE SUBTRACT THE WIND SPEED)
Next, add eq1 and eq2 and we get:
2r=220 divide each side by 2
r=110 mph --------------------------rate of plane in calm air
substitute r=110 into eq1
110+w=120 subtract 110 from each side
110-110+w=120-110 collect like terms
w=10 mph-----------------------------------rate of the wind
CK
5=600/(110+10)
5=600/120
5=5
and
6=600/(110-10)
6=600/100
6=6