Hello everyone

I'm sure that what bilalsaeedkhan meant to say was: Originally Posted by

**bilalsaeedkhan** The grade is actually the slope of the railroad line. So the given slopes are 0.03 and 0.02. Calculate the length required for each slope and subtract the answers to get your final answer which is the additional length of track required. Slope is the change is height over change in length.

1) For a slope of 0.03 and height of 600ft (which is same for both cases), the length required is 30000ft. Grandad says: 20000 ft

2) For a slope of 0.02 and height of 600ft, the length required is 20000ft Grandad says: 30000 ft

So 30000-20000= 10000 ft, which is your final answer. The answer to the question is "a" 10000ft.

The grade is sometimes defined as

$\displaystyle \text{grade = }\dfrac{\text{rise}}{\text{run}}$

So for the first calculation, if the run (the length of track required) is $\displaystyle \displaystyle x$, then:

$\displaystyle \displaystyle 0.03 = \frac{600}{x}$

$\displaystyle \displaystyle \Rightarrow x = \frac{600}{0.03}$

$\displaystyle =20000$

Is that OK now?

Grandad