please tell me if these are right.
Soybean meal is 12% protein, cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240-lb. mixture that is 11% protein? 80 pounds soybean and 160 pounds of cornmeal
Trains A and B are traveling in the sme direction on parallel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 90 miles per hour. Train A passes a station at 4:10 pm. If train B passes the same station at 4:22PM, at what time will train B catch up to train A? The answer is 5:58
S+C=240
.12S+.06C=.11*240
Your answer is wrong.
ok, the initial distance between them is 12min/60min*80miles=16miles check that.
Now how long does the trainB take to catch up: distance/relative velocity
= 16miles/10mph=1.6hr or 1hr36min or
you got it right.
To solve the first problem, we need to set up an equation based on the given information. Let's assume x represents the pounds of soybean meal and y represents the pounds of cornmeal.
We know that the total weight of the mixture is 240 pounds, so we have the equation:
x + y = 240
The protein content in soybean meal is 12%, which means 0.12x pounds of protein come from soybean meal. Similarly, cornmeal has a 6% protein content, so 0.06y pounds of protein come from cornmeal. The total protein content in the mixture is 11%, which means 0.11 * 240 = 26.4 pounds of protein. We can create another equation for the protein content:
0.12x + 0.06y = 26.4
Now we have a system of equations:
x + y = 240
0.12x + 0.06y = 26.4
To solve the system, we can use substitution or elimination methods. Let's use the substitution method in this example.
From the first equation, we have x = 240 - y. Substituting this value into the second equation gives:
0.12(240 - y) + 0.06y = 26.4
Simplifying the equation:
28.8 - 0.12y + 0.06y = 26.4
28.8 - 0.06y = 26.4
-0.06y = -2.4
y = -2.4 / -0.06
y = 40
Substituting the value of y back into the first equation:
x + 40 = 240
x = 240 - 40
x = 200
So, the correct solution is 200 pounds of soybean meal and 40 pounds of cornmeal.
For the second problem, we need to find the time at which train B catches up to train A. We know that train B passes the station at 4:22 PM, 12 minutes after train A. The two trains have a relative speed of 90 - 80 = 10 miles per hour.
To calculate the time it takes for train B to catch up to train A, we need to find the distance they both travel during that time. The distance travelled will be the same for both trains when they meet.
Since train B travels for 12 minutes longer, we can convert this time into hours by dividing it by 60:
12 minutes / 60 = 0.2 hours
Now, we can calculate the distance using the formula: distance = speed * time.
Distance traveled by train B = 10 miles per hour * 0.2 hours = 2 miles
Since train A passes the station at 4:10 PM and train B catches up after 2 miles, we can calculate the time it took for train A to travel 2 miles:
2 miles / 80 miles per hour = 0.025 hours
To find the time when train B catches up to train A, we need to add the time it took for train A to travel 2 miles to the original time of 4:10 PM:
4:10 PM + 0.025 hours = 4:10 PM + 1 minute and 30 seconds = 4:11 PM and 30 seconds
Therefore, the correct answer is 4:11 PM and 30 seconds.