6. To determine the RPM (Rotations Per Minute) at which the other gear is running, we can use the concept of gear ratios. The gear ratio is the ratio of the number of teeth on the driving gear to the number of teeth on the driven gear.
In this case, we have a 36-tooth gear driving a 64-tooth gear. The gear ratio is given by the ratio of the driven gear teeth to the driving gear teeth:
Gear Ratio = Number of teeth on driven gear / Number of teeth on driving gear
Gear Ratio = 64 / 36 = 1.7778 (approximately)
Since the gear ratio represents the ratio of RPMs, we can find the RPM of the other gear by multiplying the gear ratio by the RPM of the driving gear:
RPM of other gear = Gear Ratio * RPM of driving gear
RPM of other gear = 1.7778 * 280
RPM of other gear ≈ 498.89
Therefore, the other gear is running at approximately 498.89 RPM.
7. If three men complete a certain job in 8 days, and assuming they all work at the same speed, we can calculate the amount of work done per day by a single man.
Let's denote the amount of work done by a single man in one day as "D." Since three men complete the job in 8 days, the total work done is 3D (3 men working for 8 days).
Now, if 7 men were to complete the same job, and assuming they all work at the same speed, we can calculate the number of days required.
The amount of work done by 7 men in one day is 7D. Since the total work required remains the same, we can set up the following equation:
3D (work done by 3 men in 8 days) = 7D (work done by 7 men in x days)
By equating the amounts of work done, we can solve for "x":
3D * 8 = 7D * x
24 = 7x
x ≈ 3.43
Therefore, it would take approximately 3.43 days for 7 men to complete the same job, assuming they all work at the same speed.