Determine rational expression

Question

Can somebody help me with the following word problems:

Problem #1

Russel's combine can clear a field in 24 tractor hours. Jerome's combine can clear the same field in 30 hours. If they work together how long would it take?

The answer is supposed to be $\frac{40}{3}$ or $13.33$... hours, but I have no clue what the equation would be.

Problem #2

During part of a trip from Albany, New York to Missoula, Montana, Jeff's average driving speed is 5km/h faster than Xavier's. Jeff and Xavier each drive for 10 hours. Altogether, they drive 2010 km. On average, how fast does each drive?

I came up with this equation but I don't think it's right:

$$10(x+5) + 10x = 2010$$

The answer in the book says $x = -1,3,4,5$ and $y = 27$.

Any ideas?

Answer 1

1. The answer is $$\frac{1}{\frac{1}{24}+\frac{1}{30}}$$

I'll leave it to the reader to figure out why. (Hint: it involves $rate=\frac{work}{time}$)

2. Your equation is correct: $distance=speed\times time$

Answer 2

Your equation for the second problem is correct. For the first problem, it's helpful to first answer the following problem:

How much of the field can each of them clear in one hour?

so that we measure in how many (fractions of) fields per hour they can clear, rather than how many hours per field it takes.