A plane flying at 300mph...

Question

A plane flying at 300mph has a 3-hour headstart on a "chase plane" that has a speed of 800mph. How far from the airport will the chase plane over take the first plane?

Answer 1

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Answer 2

Hi 

 

Your planes are travelling at different rates, and will meet up just once when the faster plane flies by. when that happens, they will have traveled the same distance. find the equation for the first plane:

let D = distance, and t = time in hours

D= 300 * t  

the second planes is travelling faster:

D = 800 * t

 

we also have to account to the head start of the first plane, which is 3 hours at 300 miles per hour:

D = 300 * 3= 900 miles. 

Now modify that first equation by adding 900 miles:

D = (300 * t) + 900.        I put the original equation in parenthesis.

 

We know the planes will  meet at some distance from the airport. This means they will be equal distance away from that airport, and we can set the equations equal to each other:

(300 t) +900= 800 *t

300t +900 = 800 t

 

now we must get the t's on one side. Subtract 300t from both sides: you know to do this because you see the plus (or minus) sign. Do those first

300t +900 = 800t

-300t           -300t

___________________

0       +900= 500t     now all the  t's are on one side

 

to get t by itself, multiply the reciprocal of the number being multiplied by t.

A reciprocal is a flipped fraction such as 3/4 becomes 4/3 . Whole numbers like 500 can also be written as 500/1.  so its reciprocal is 1/500.

so to solve for t, we must multiply both sides by 1/500.

 

   1                          1

_____ *900    =       ____  *500t

500                        500

 

900/500 = t *500/500

1.8 hours =t (labels help keep track. we need distance, so we are not quite done.

 

now we take 1.8, which is the number of hours, and plug it into either equation. to check your answer, plug it into both. they should be the same.

 

300 t + 900= 300* 1.8 + 900 =540 + 900 =1440 miles (there's the label we need)

plugging into the second equation,we have 800 * t = 800 * 1.8 =1440 miles.

 

the answers match, so I am confident we have solved this problem correctly.