Thread: More help with quadratic equation word problems...

Sorry for posting two threads but I can't seem to figure these out.

1)An express train makes the run between two cities 250km apart in 1.25h less than a local train whose speed is 10km/h less. Find the average speed of the express

2)A farmer has a rectangular field 400m by 500m. On this field a uniform strip on the outside will be left unplanted so that half of the total area will be planted. How wide is the strip?

Thanks so much to whoever took the time to read these

Originally Posted by stephie

1)An express train makes the run between two cities 250km apart in 1.25h less than a local train whose speed is 10km/h less. Find the average speed of the express

Let the speed of the express be e, and log the local train be s.

The time that the express takes is t_e = 250/e, and the time the local train takes is t_s = 250/s. As s = e - 10 we are left with:

t_e = 250/e,

and

t_s = 250/(e-10).

We are also told that:

t_e = t_s - 1.25,

so we have:

250/e = 250/(e-10) - 1.25.

Multiply through by e(e-10) to get:

250 (e-10) = 250 e - 1.25 e (e-10)

which simplifies to the quadratic:

1.25 e^2 - 12.5 e - 2500 = 0,

which has roots e=50 and e=-40, but as e should be positive we find
e=50.

RonL

Originally Posted by stephie

...
2)A farmer has a rectangular field 400m by 500m. On this field a uniform strip on the outside will be left unplanted so that half of the total area will be planted. How wide is the strip?...

Hello, stephie,

I've attached a diagram of the field.

Let x be the width of the strip with 0 ≤ x ≤ 200. Then the area of the strip is:
4x² at the 4 corners
2*x(500 - 2x) two rectangles at the longer sides of the field
2*x(400 - 2x) two rectangles at the shorter sides of the field

4x² + 2*x(500 - 2x) + 2*x(400 - 2x) = ½*400*500

4x² + 1000x - 4x² + 800x - 4x² = ½*400*500

-4x² + 1800x - 100,000 = 0. Solve the quadratic equation for x:

x = 225 ± 25*√(41)

x ≈ 385.08 m (this value doesn't belong to the domain) or x ≈ 64.92 m

EB