Plane Algebra Help

Question

A plane flying the 3458-mi from New York City to London has a 40-mph tailwind. The flight's point of no return is the point at which the flight time required to return to New York is the same as the time required to continue to London. If the plane's speed in still air is 840 mph, how far is New York from the point of no return?

Answer 1

Flying with the tail wind, the speed the plane is travelling is 880mph. Flying against the wind, the rate would be 800mph.

 

At this point of no return, the distance left can be represented by 3458-880t.

The distance to get back 880t.

 

So            rate     *   time     = distance ( you can now fill in the rate and distance and divide to get an expression for time

 

going         880       (3458-880t)/880       3458-880t

returning    800       (880t)/800                880t

 

So the 2 times must be equal from the description of the problem

 

(3458 - 880t)/ 880 = 880t/800     cross multiply

2766400 - 704000t = 774400t

2766400              = 1478400 t

1.87121212         = t

That's 1 hours and 52 minutes.

 

Let's check.

t=1.8712121212 hours

880 t =  miles or 1646.666666 miles which would take 1811.3333/880 =2.0583 hours.

Travelling 1646.6666 miles back at 800 mph would be 1646.6666/800 = 2.0583 hours.

So the distance from NYC is 1646.6666

So the answer is correct.

 

Another way of thinking about the problem is by imagining that you are at this point....d miles from london and 3458-d miles from new york.

 

So d/880 is the time to london. (3458-d)/800 is the time to new york

So 800 d = 880(3458-d)

     1680d = 3043040

            d = 1811.3333

 

This is the distance from the point of no return to london. This is the same number we had above.

So 3458-1811.3333 = 1646.6666 miles from NYC.

 

Hope this helped.