Answer:
t = 13 hours
The values will be equal in 10 years.
Step-by-step explanation:
Three
There are two ways to do this problem. I'll do it the simplest way -- which will benefit you most if you are about to take a physics class.
Follow these observations.
- The difference of speed of these two cars is 70 - 65 = 5 mph
- The distance travelled by the first car before the second one starts is 65 miles in 1 hour. That comes about because Tom goes 65 miles before Michelle even starts. She starts exactly 1 hour after Tom and he has gone 65 miles in that time.
- She is going faster, but he is still moving. That's what makes the problem hard.
- Fortunately, you don't have to figure that out. You have all the information you need.
Solution
Time it takes to Catch Tom = distance to be made up / difference in speed
Distance to be made up = 65 miles
Difference in speed = 5 mph
Time taken for michelle to catch Tom = t
t = 65/5
t = 13 hours.
Solution Two
The distance is the same when Michelle catches Tom
d = r*t
Michelle's rate = 70 mph
Michelle's time = t
Tom's rate = 65
Tom's Time = t + 1
70 * t = 65(t + 1)
70 * t = 65*t + 65
70*t - 65*t = 65
5t = 65
t = 65/5 = 13
In thirteen hours, Michelle will catch Tom
Four
One house increases by 10000 the other decreases by 5000. You could do it using the first method above, but in this case the second is actually easier.
Juan: 200000 + 10000*t
Tia : 350000 - 5000t
When will the be equal (at what price and when?).
200000 + 10000t =350000 - 5000t Divide by 1000
200 + 10t = 350 - 5t Add 5t to both sides
200 + 10t + 5t = 350 Combine
200 + 15t = 350 Subtract 200 from both sides
15t = 150 Divide by 15
t = 150/15
t = 10 years
