Thread: Does not compute!

A word problem is given which I've answered correctly, but a second question doesn't add up. The problem is:

A North-South highway intersects an East-West highway at a point P. An automobile crosses P at 10:00 AM, traveling east at a constant rate of 20 mph. At that same instant another automobile is two miles north of P, traveling south at 50 mph. Find a formula which expresses the distance d between the automobiles at time t (hours) after 10:00 AM. At what time will the automobiles be 104 miles apart?

My answer, which the book confirms, is



To answer the second question, I started with









Using the Quadratic Formula, I get



which I can only reduce to



But the answer given in the book is:



So how do I get there? Did I make a mistake along the way?

Hello,earachefl!

A North-South highway intersects an East-West highway at a point .
An automobile crosses at 10:00 AM, traveling east at a constant rate of 20 mph.
At that same instant another automobile is two miles north of , traveling south at 50 mph.
(a) Find a formula which expresses the distance between the automobiles
. . .at time (hours) after 10:00 AM.
(b) At what time will the automobiles be 104 miles apart?

I don't agree with either of their answers . . .

Code:

          Q *
            |
        50t |
            |
          B *
            |  *   d
      2-50t |     *
            |        *
      - - P * - - - - - * - -
            |    20t    A
            |

At 10 AM, the first car is at point .
. . hours later, it is at point

At 10 AM, the second car is at point .
. . hours later, it is at point .
. . Hence: .

Pythagorus says: .

(a) Then we have: .


If

Square both sides: .

Divide by 4: .

Quadratic Formula: .

. .


And the positive root is: .