How Fast Did the Plane Fly from Glasgow to Halifax?

[cleeoo27]

Homework Statement

A plane flew 4200 km from Glasgow to Halifax into a head wind. With a tail wind, the plain flew 100km/h faster on the return trip. The total flying time from Glasgow to Halifax and back was 13 h. What was the flying speed from glasgoq to Halifax?

The Attempt at a Solution

Speed x Time = Distance

G-H x 4200/x 4200

H-G x+100 4200/(x+100) 4200

TOT 13h

4200/x + 4200/(x+100) = 13 x (x)(x+100)

4200(x+100) + 4200 (x) = (13)(x)(x+100) ...


I kept doing this but none of these type of problems turn out right with me.

 

[Dick]

Looks good so far. It's just a quadratic equation. Keep going.

 

[VietDao29]

Homework Statement

A plane flew 4200 km from Glasgow to Halifax into a head wind. With a tail wind, the plain flew 100km/h faster on the return trip. The total flying time from Glasgow to Halifax and back was 13 h. What was the flying speed from glasgoq to Halifax?

The Attempt at a Solution

Speed x Time = Distance

G-H x 4200/x 4200

H-G x+100 4200/(x+100) 4200

TOT 13h

4200/x + 4200/(x+100) = 13 x (x)(x+100)

4200(x+100) + 4200 (x) = (13)(x)(x+100) ...


I kept doing this but none of these type of problems turn out right with me.

Oh, at first, looking at your post, it seems like a mess, and I have to quote it for easier reading. If you want to post things that needs "columns", and "rows", you can use the CODE tag, it's the sharp sign (i.e, #), it'll be much clearer. Like this:

The Attempt at a Solution

             Speed    x   Time     =     Distance

G-H         x             4200/x           4200

H-G         x+100      4200/(x+100)        4200

TOT                         13h

See? :)

Back to your problem, the reddened line is wrong. It should have read:

4200/x + 4200/(x+100) = 13

Then, we multiply both sides by x(x + 100) to obtain your last line:

4200(x + 100) + 4200x = 13 x(x + 100)

Now, just expand everything out, isolate them to one side, and it's just a quadratic equation. :)