Two planes start from the same airport at the same time and travel in opposite directions. If the first plane travels at an average speed of 240 mph and the second plane travels at an average speed of 320 mph, in how many hours will the planes be 1,400 miles apart?
The ratio of John's money to Fred's money is 8:3. If John gives Fred $6, John will have twice as much money as Fred. How much money does John have before he gives Fred the money?
two motorists start toward each other from cities 400 miles apart at 1 pm. If one motorist travels at an average rate of 42 miles per hour and the other motorist travels at an average rate of 38 mph, at what time will the cars meet.
Please show your work on how you got the answer.
The ratio of John's money to Fred's money is 8:3. If John gives Fred $6, John will have twice as much money as Fred. How much money does John have before he gives Fred the money?
two motorists start toward each other from cities 400 miles apart at 1 pm. If one motorist travels at an average rate of 42 miles per hour and the other motorist travels at an average rate of 38 mph, at what time will the cars meet.
Please show your work on how you got the answer.
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1. For this problem, I wrote and solved the following equation:
320t + 240t = 1400
560t = 1400
t= 2.5 hours
Check if this makes sense:
In 2.5hours plane 1 travelling at 240mph traveled 240mph*2.5hours = 600miles. In the same amount of time plane 2 travelling at 320mph traveled 320mph*2.5hours = 800 miles. The distance between the two planes after 2.5hours is 600 + 800 = 1400 miles: we're good!
2. We are told that the ratio of John's money to Fred's money is 8:3. From this, we can represent the amount of money John has as 8x and the amount of money that Fred has as 3x. The second step in solving this problem is to write an equation for what happens when John gives Fred 6$. If John gives Fred 6$ (ie 8x-6), then the amount of money that John will have will be twice that of what Fred now has (ie 2*amount of money Fred has after receiving 6$ = 2(3x+6)):
8x - 6 = 2(3x + 6)
Now we can solve for x:
8x - 6 = 6x + 12
2x = 18
x = 9
To find the amount of money that John had before he gave Fred the money, plug in x = 9 into the original expression for the amount of money John has, 8x.
320t + 240t = 1400
560t = 1400
t= 2.5 hours
Check if this makes sense:
In 2.5hours plane 1 travelling at 240mph traveled 240mph*2.5hours = 600miles. In the same amount of time plane 2 travelling at 320mph traveled 320mph*2.5hours = 800 miles. The distance between the two planes after 2.5hours is 600 + 800 = 1400 miles: we're good!
2. We are told that the ratio of John's money to Fred's money is 8:3. From this, we can represent the amount of money John has as 8x and the amount of money that Fred has as 3x. The second step in solving this problem is to write an equation for what happens when John gives Fred 6$. If John gives Fred 6$ (ie 8x-6), then the amount of money that John will have will be twice that of what Fred now has (ie 2*amount of money Fred has after receiving 6$ = 2(3x+6)):
8x - 6 = 2(3x + 6)
Now we can solve for x:
8x - 6 = 6x + 12
2x = 18
x = 9
To find the amount of money that John had before he gave Fred the money, plug in x = 9 into the original expression for the amount of money John has, 8x.
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