Question

Mr. Hall has two combines to harvest 625 acres of corn. One combine has a 12 row header and the other has an 8 row header. The combine with the 12 row header harvests 11.8 acres per hour using 1.5 gallons of diesel fuel per acre. At the same time, the combine with the 8 row header harvests 8.1 acres per hour using 1.4 gallons of diesel fuel per acre.a. Using both combines, how many acres do they harvest in an hour?b. How many hours does it take them to harvest his corn?C. How many acres does each combine harvest?d. How many gallons of diesel fuel are used?

Answer 1

a. 19.9 acres per hour

b. 31.41 hours

c. 1st Combine: 370.6 acres

2nd Combine: 254.4 acres

d. 912.06 gallons

Step-by-step explanation:

The first combine has a 12-row header and harvests 11.8 acres per hour using 1.5 gallons of diesel per acre.

The 2nd combine has an 8-row header and harvests 8.1 acres per hour using 1.4 gallons of diesel per acre.

Then, if we use both combines, the number of acres harvest in an hour can be calculated as the sum of the rate of each combine, so:

11.8 acres per hour + 8.1 acres per hour = 19.9 acres per hour

Now, we can use this rate (19.9 acres per hour) to know the number of hours to harvest 625 acres of corn as:

`625\text{ acres }*\frac{1\text{ hour}}{19.9\text{ acres}}=31.41\text{ hours}`

So, both combines take 31.41 hours to harvest all the corn.

To know how many acres each combine harvest, we will use the total number of hours and the rate of acres per hour for each combine.

So, for the first combine, we get:

`31.42\text{ hours}*\frac{11.8\text{ acres}}{1\text{ hour}}=370.6\text{ acres}`

For the second combine, we get:

`31.42\text{ hours}*\frac{8.1\text{ acres}}{1\text{ hour}}=254.4\text{ acres}`

Finally, to know the total number of gallons used, we need to know the number of gallons for each combine.

So, for the first combine (1.5 gallons per acre), we get:

`370.6\text{ acres}*\frac{1.5\text{ gallons}}{1\text{ acre}}=555.9\text{ gallons}`

For the second combine (1.4 gallons per acre), we get:

`254.4\text{ acres}*\frac{1.4\text{ gallons}}{1\text{ acre}}=356.16\text{ gallons}`

Then, the total number of gallons of diesel fuel used were:

555.9 gallons + 356.16 gallons = 912.06 gallons of diesel.

So, the answers are:

a. 19.9 acres per hour

b. 31.41 hours

c. 1st Combine: 370.6 acres

2nd Combine: 254.4 acres

d. 912.06 gallons