A student on her way to spring break

Question

A student on her way to spring break vacation drive from her home to the airport at an average speed of 40 mph. The student spent a total of 60 minutes at the airport before her airplane lifted off. The airplane flew from her airport to her destination at an average speed of 440 mph. The entire distance was 1360 miles; the entire trip took four hours. Find the distance from the airport to the student's home to the nearest mile.

Answer 1

distance=rate x time

d=rt

let t=the time from home to the airport

40t+440(4-t)=1360

40t+1760-440t=1360

1760-400t=1360

-400t=1360-1760

-400t=-400

t=1 hour

d=rt

d=40(1)

d=40 miles

 

Answer 2

I think we need to assume that the "entire trip taking 4 hours" does not include the 60 minutes at the airport.  If it did, the actual time spent traveling would be 3 hours and even at 440 mph, she would not make it 1,360 miles.

 

So, assuming she spent 4 hours traveling (in the car or on the airplane), we proceed as follows:

 

Here, we will have a system of 2 equations with 2 unknowns.

 

Let t1 = time traveled from her home to the airport

Let t2 = time traveled from the airport to her destination

 

Using the formula Distance = Rate * Time, we get:

 

(40)t1 + (440)t2 = 1360

 

Since we know the entire trip took 4 hours, we get:

 

t1 + t2 = 4

 

Now we can solve for t2 and plug it back into the first equation:

 

t2 = 4 - t1

 

 

(40)t1 + (440)(4 - t1) = 1360

1760 - 400 t1 = 1360

t1 = 1

 

So the distance from her home to the airport is:

 

(40)(1) = 40 miles

 

 

J.T.