SOLUTION: An airplane leaves Los Angeles for Denver at a speed of 410 miles per hour (mph). Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: An airplane leaves Los Angeles for Denver at a speed of 410 miles per hour (mph). Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 3379: An airplane leaves Los Angeles for Denver at a speed of 410 miles per hour (mph). Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 530 mph. When they meet, how far are they from Denver?
Answer by drglass(89) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this problem, you need to state it mathematically. First, state the facts:


  1. The distance from Denver to LA is 850 miles

  2. The plane from Denver to LA flies at 410 mph

  3. The plane from LA to Denver flies at 530 mph

  4. The plane from LA starts 1%2F2 hour earlier


Now let's restate these mathematically:


  1. Lst t be the time the second plane has been flying, in other words, the first plane took of t+-+1%2F2 hours ago

  2. D = 850 miles, where D is the distance from LA to Denver

  3. the distance travelled by plane from Denver to LA is 410t

  4. the distance travelled by plane from LA to Denver is 530t

  5. the distance the first travelled before the second plane took off is 1%2F2+%2A+410+=+205 miles, so the distance between them at time t is 850 - 205 = 645 miles


The planes meet when the distances they travelled adds up to 645 (the distance they were from each other at time t). Using the expressions for distance above, this gives us the equation 410t+%2B+530t+=+645 or 940t+=+645. The time at which the planes meet up is t+=+645%2F940+%7E+0.6862. The distance from Denver travelled by the first plane is 205+%2B+410+%2A0.6862+=+486.3. The distance travelled by the first plane is 530%2A0.6862+=+383.7 miles from LA. This is 850+-+383.7+=+486.3 miles from Denver. They passed each other 486.3 miles from Denver.