two trains start from towns 208 miles apart and travel towards each other on parallel tracks. They pass each other 1.6 hours later. If one travels 10 mph faster than the other find the speed of each train?
Sum of speeds = 208 miles/1.6hr=130 mph
Difference of speeds = 10 mph
Faster train = (sum+difference)/2 mph
Slower train = (sum-difference)/2 mph
Explanation:
let f=faster train, s=slower train
S=sum, D=difference, then
S=f+s
D=f-s
Add:
(S+D)=f+s+f-s=2f
therefore f=(S+D)/2
Simlarly, by subtracting,
S-D = f+s - (f-s) = 2s
therefore s=(S-D)/2
fast 70mph
slow 60 mph
To find the speed of each train, we can set up a system of equations using the given information.
Let's call the speed of one train "x" mph. Since the other train is traveling 10 mph faster, we can represent its speed as "x + 10" mph.
Now, let's consider the distance traveled by each train. Train A travels for 1.6 hours at a speed of "x" mph, so its distance is given by: Distance_A = x * 1.6.
Similarly, Train B travels for 1.6 hours at a speed of "x + 10" mph, so its distance is: Distance_B = (x + 10) * 1.6.
Since the two trains start from towns located 208 miles apart and pass each other, the sum of their distances should be equal to this initial distance:
Distance_A + Distance_B = 208.
Plugging in the expressions for Distance_A and Distance_B, we get:
x * 1.6 + (x + 10) * 1.6 = 208.
Simplifying the equation:
1.6x + 1.6(x + 10) = 208,
1.6x + 1.6x + 16 = 208,
3.2x + 16 = 208,
3.2x = 192.
Dividing both sides of the equation by 3.2:
x = 60.
Therefore, one train is traveling at a speed of 60 mph, and the other train is traveling at a speed of 60 + 10 = 70 mph.