I'm stuck on a few problems.
1) If an ant travels $50$ cm per second and decides to travel 2760 miles, how many days would it take to arrive to their destination?
First, I converted miles to centimeters. $1$ mi $=160934$ cm, so $2760$ mi is $4.4417784 \times 10^8$. With $t$ representing our time in seconds, I have $$(4.4417784 \times 10^8)=50t \\ t= 8.883568 \times 10^7 \ \text{seconds}$$
Converting this to days, $$\cfrac{(8.883568 \times 10^7)}{60 \times 60 \times 24} \\ \approx 10.28 \text{ days}$$
But I'm marked wrong here, so I must have made a mistake. The answer doesn't even look remotely correct because it seems too low.
2) The Sahara Desert has an area of approximately $9,400,400$ km$^2$. While estimates of its average depth vary, they center around $150$ m. One cm$^3$ holds approximately $8,000$ grains of sand.
a) Approximately how many grains of sand are in the Sahara Desert?
b) Express your answer to part a) in millions of grains of sand.
c) What fraction of the Sahara is made by $1$ grain of sand (select units for your solution as well)?
d) A small dump truck can carry approximately $20.5$ m$^3$ of sand. Suppose a long line of dump trucks were to dump a load of sand every $30$ seconds. How many years would it take to re-create the Sahara Desert?
a) Here I converted 150 m to km, which got me 0.15 km for the deserts depth. Then I figured I needed to know how many times 0.15 goes into the area. This is $62,669,333.33$ or ${6.266933333 \times 10^7}$. At this point I'm not sure how to account for the fact that 1/100,000 km holds 8,000 grains of sand.
b) I can't attempt this problem without knowing the answer to a)
c) $150$ m to km $= 0.15$ km. The area * 0.15 should get me the total amount of sand, so $\cfrac{1}{6.266933333 \times 10^7}$ should be our answer. I was marked correct, at least.
d) I can't answer this without knowing a), either. I think I have an idea how to solve it if I knew the first answer. If V was the amount of sand in total and x was our time in seconds, then I just take the rate per second instead of per 30 seconds and say $41x/60 = V$, then after solving for x I express it in years, right?
Can I get some help?
Hint:
1) Check your calculations
2) I assume that the desert is shaped like a cuboid. The area is $9{,}400{,}400\mathrm{km^2} = 9.4004\times10^{16}\mathrm{cm^2}$. The depth is $150\mathrm m = 15{,}000\mathrm{cm}$. The volume of the cuboid is then $1.41006\times10^{21}\mathrm{cm^3}$. If $1\mathrm{cm^3}$ contains $8{,}000$ grains of sand, then how many does the total volume of the desert contain?