I likey my new sig. This isn't game related. Talk about your siggys here. Or avatars. It be art discussion class. Wait, dod't do that. Talk about which superpower you'd like. And how'd you use it. I'd be invisible.. txet siht ekil tsuJ
Train A, traveling 70 miles per hour (mph), leaves Westford heading toward Eastford, 260 miles away. At the same time Train B, traveling 60 mph, leaves Eastford heading toward Westford. When do the two trains meet? How far from each city do they meet?
To solve this problem, we'll use the distance formula:
Distance = Rate x Time
Since an equation remains true as long as we perform the same operation on both sides, we can divide both sides by rate:
Distance
---------- = Time
Rate
or by time:
Distance
---------- = Rate
Time
So rate is defined as distance divided by time, which is a ratio.
Speed is another word that is used for rate. When a problem says that a train is moving at a speed of 40 mph, you can understand this to mean that the train's rate is 40 mph, which means it will travel 40 miles in one hour.
Here are two different ways to approach this problem. Let's start by listing the information given:
Speed of Train A: 70 mph
Speed of Train B: 60 mph
Distance between Westford and Eastford: 260 miles
Method I: We'll use the notion of relative speed 1 (or relative rate) in order to express the rates of the two trains in one number that can then be used in the distance formula.
Imagine you're on Train A. You're going 70 mph, so your speed relative to the trees, houses, and other non-moving things outside the train is 70 mph. (All of those objects look as if they're going by at 70 mph.) Now imagine you're the engineer and you can see Train B coming toward you - not on the same track, of course! Since Train B is moving 60 mph, it will look as if it's approaching faster than if it were sitting still in the station - a lot faster than the trees and houses appear to be moving.
The relative speed of the two trains is the sum of the speeds they are traveling. (If you're on either of the trains, this is the speed you appear to be moving when you see the other train.) In our problem, the relative speed of the two trains is 70 mph + 60 mph = 130 mph. What if the trains were traveling in the same direction? Then we'd need to subtract the speed of the slower train from the speed of the faster train, and their relative speed would be 10 mph.
At this point we know two of the three unknowns: rate and distance, so we can solve the problem for time. Remember that time = distance/rate, the distance traveled is 260 miles, and the relative speed is 130 mph:
t = 260 miles/130 mph
t = 2 hrs.
We find that the trains meet two hours after leaving their respective cities.
Method II: Here we'll begin by noting that the distance between Westford and Eastford is 260 miles: this is the total distance the trains will travel. Using the distance formula (Distance = rate x time, or D = rt) we can express the distance traveled by each train:
Train A moving at 70 mph in t hours will cover 70t miles
Train B moving at 60 mph in t hours will cover 60t miles
Together the two trains will cover the distance 70t + 60t
Since we know that this distance is 260 miles, we can write the following algebraic equation to represent this information.
70t + 60t = 260
Solving this equation we find that:
130t = 260
t = 2
which tells us that the trains will meet in 2 hours.
I likey my new sig. This isn't game related. Talk twas something abouabout your siggys here. Or avatars. It be art discussion class. Wait, dod't do that. Talk about which superpower you'd like. And how'd you use it. I'd be invisible.. txet siht ekil tsuJ
Train A, traveling 70 miles per hour (mph), leaves Westford heading toward Eastford, 260 miles away. At the same time Train B, traveling 60 mph, leaves Eastford heading toward Westford. When do the two trains meet? How far from each city do they meet?
To solve this problem, we'll use the distance formula:
Distance = Rate x Time
Since an equation remains true as long as we perform the same operation on both sides, we can divide both sides by rate:
Distance
---------- = Time
Rate
or by time:
Distance
---------- = Rate
Time
So rate is defined as distance divided by time, which is a ratio.
Speed is another word that is used for rate. When a problem says that a train is moving at a speed of 40 mph, you can understand this to mean that the train's rate is 40 mph, which means it will travel 40 miles in one hour.
Here are two different ways to approach this problem. Let's start by listing the information given:
Speed of Train A: 70 mph
Speed of Train B: 60 mph
Distance between Westford and Eastford: 260 miles
Method I: We'll use the notion of relative speed 1 (or relative rate) in order to express the rates of the two trains in one number that can then be used in the distance formula.
Imagine you're on Train A. You're going 70 mph, so your speed relative to the trees, houses, and other non-moving things outside the train is 70 mph. (All of those objects look as if they're going by at 70 mph.) Now imagine you're the engineer and you can see Train B coming toward you - not on the same track, of course! Since Train B is moving 60 mph, it will look as if it's approaching faster than if it were sitting still in the station - a lot faster than the trees and houses appear to be moving.
The relative speed of the two trains is the sum of the speeds they are traveling. (If you're on either of the trains, this is the speed you appear to be moving when you see the other train.) In our problem, the relative speed of the two trains is 70 mph + 60 mph = 130 mph. What if the trains were traveling in the same direction? Then we'd need to subtract the speed of the slower train from the speed of the faster train, and their relative speed would be 10 mph.
At this point we know two of the three unknowns: rate and distance, so we can solve the problem for time. Remember that time = distance/rate, the distance traveled is 260 miles, and the relative speed is 130 mph:
t = 260 miles/130 mph
t = 2 hrs.
We find that the trains meet two hours after leaving their respective cities.
Method II: Here we'll begin by noting that the distance between Westford and Eastford is 260 miles: this is the total distance the trains will travel. Using the distance formula (Distance = rate x time, or D = rt) we can express the distance traveled by each train:
Train A moving at 70 mph in t hours will cover 70t miles
Train B moving at 60 mph in t hours will cover 60t miles
Together the two trains will cover the distance 70t + 60t
Since we know that this distance is 260 miles, we can write the following algebraic equation to represent this information.
70t + 60t = 260
Solving this equation we find that:
130t = 260
t = 2
which tells us that the trains will meet in 2 hours.
Now, where do the trains meet? We again use the distance formula to find how far each train has traveled in two hours:
For Train A: 70 mph x 2 hrs = 140 miles
For Train B: 60 mph x 2 hrs = 120 miles
Thus the two trains meet at a point 140 miles from Westford and 120 miles from Eastford. [/quote]
what are you saying i can not see what you have wrote.all i saw was something about 70.
I likey my new sig. This isn't game related. Talk about your siggys here. Or avatars. It be art discussion class. Wait, dod't do that. Talk about which superpower you'd like. And how'd you use it. I'd be invisible.. txet siht ekil tsuJ
