SOLUTION: 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
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Question 165150This question is from textbook
: 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? This question is from textbook
You can put this solution on YOUR website! 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
Hope this helps----ptaylor
