help with my algebra hw???

First lay out your information.

Train P travels 400 km at a speed of x km/h

Train F travels 330 km at a speed of (x-14) km/h (because you are told that the freight train is 14 km/h slower) You always have to set your known variable as x and your unknown in terms of x.

Next you set up a ratio:

We'll put Train P on the left of the = and Train F on the right

400 km = 330 km

_______ _______

x Km/h (x-14)km/h

Solve the ratio by cross-multiplying:

400 (x-14) = 330 x

400x - 5600 = 330 x

+5600 +5600

400x = 330x + 5600

- 330x -330x

70x = 5600

x = 80

If x = 80, then x-14 = 66

The passenger train is traveling at 80 km/h

The freight train is traveling at 66 km/h

Check by plugging your variables back into the original ratio and multiplying.

Does 330 (x) = 400 (x-14)

330 (80) = 400 (66)

26,400 = 26,400

It checks out !!

P = speed of passenger train

F = speed of freight train

F = P - 14

330/F = 400/P

330/(P-14) = 400/P

330P = 400(P-14) = 400P - 5600

70P = 5600

P = 80 km/h

80 km/h