SOLUTION: 4. Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specified variable
Question 296339: 4. Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
A plane flying the 3020-mile trip from City A to City B has a 60-mph tailwind. The flight's point of no return is the point at which the flight time required to return to City A is the same as the time required to continue to City B. If the speed of the plane in still air is 430 mph, how far from City A is the point of no return? Round your answer to the nearest mile. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A plane flying the 3020-mile trip from City A to City B has a 60-mph tailwind.
The flight's point of no return is the point at which the flight time required
to return to City A is the same as the time required to continue to City B.
If the speed of the plane in still air is 430 mph, how far from City A is the
point of no return?
Round your answer to the nearest mile.
:
Speed with the wind: 430+60 = 490
Speed against the wind: 430-60 = 370
:
Let x = dist to city A (at point of no return)
Let y = dist to city B
;
Total dist equation
x + y = 3020
y = (3020-x); use for substitution
:
A travel time equation;
Time to A = time to B, (the point of no return) =
Cross multiply
490x = 370y
Simplify divide by 10
49x = 37y
Substitute (3020-x) for y
49x = 37(3020-x)
49x = 111740 - 37x
49x + 37x = 111740
86x = 111740
x =
x = 1299.3 ~ 1299 mi from A is the point of no return
:
:
Check solution by finding the times to continue and return, should be equal:
3020 - 1299 = 1721 mi to B
1299/370 = 3.5 hr
1721/490 = 3.5 hr
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