I don't understand this question, so if anyone can answer it, that would be great!
We are doing motion problems, so as you probably know, the formula is d=rt.
(distance equals rate times time.) We have to make a chart to answer the following question...
A roller coaster goes down the first grade eight times faster than it goes up the other side. If the distance down the hill is 100 feet more than the distance up the hill and if it takes 70 seconds to go up and 10 seconds to go down, what is the speed in feet per second of the roller coaster when it goes up the hill and when it comes down the hill?
If you can answer this, thank you SO much! :)
My question is in the first line
where was the speed of the roller coaster measured when going down? At the bottom? AT the middle?
Where was the speed of the roller coaster measured going upwards?
Saying it went down the first grade 8 times faster than going up is not very specific.
thats the exact copy of the problem...so i don't have anymore information. :(
To find the speed of the roller coaster when it goes up the hill and when it comes down the hill, we can create a chart to organize the given information.
Let's define:
- rate up the hill: r
- rate down the hill: 8r (eight times faster than going up)
- time up the hill: 70 seconds
- time down the hill: 10 seconds
- distance up the hill: d
- distance down the hill: d + 100 feet (100 feet more than going up)
Now, we can fill out the chart:
Up the hill:
Rate (r) Time (t) Distance (d)
----------------------------------------------------
r 70 d
Down the hill:
Rate (8r) Time (t) Distance (d + 100)
----------------------------------------------------
8r 10 d + 100
Using the formula distance = rate × time (d = rt), we can fill out the missing values in the chart:
Up the hill:
Rate (r) Time (t) Distance (d)
----------------------------------------------------
r 70 r × 70 = 70r
Down the hill:
Rate (8r) Time (t) Distance (d + 100)
----------------------------------------------------
8r 10 (8r) × 10 = 80r (d + 100) = 80r
Now, we can set up an equation using the given information to solve for the rate:
80r = 70r + 100
By subtracting 70r from both sides:
10r = 100
Dividing both sides by 10:
r = 10
Therefore, the rate at which the roller coaster goes up the hill is 10 feet per second.
To find the rate at which it comes down the hill, we can substitute r with 10 in the chart:
Down the hill:
Rate (8r) Time (t) Distance (d + 100)
----------------------------------------------------
8(10) 10 80
Therefore, the rate at which the roller coaster comes down the hill is 80 feet per second.