Locomotive A travels 100km/hr and locomotive B travels 140km/hr. Locomotive B starts 15 kilometers Behind locomotive A and travels on the same direction.
Find the time elapsed and how far each traveled before they meet.
v(B)t-v(A)t=15
t=15/(v(A) –v(B)) = 15/(140-100)=0.375 h = 22.5 min
s(A) = v(A)t=100•0.375 =37.5 km,
s(B) = v(B)t=140•0.375=52.5 km
thanks you!
To solve this problem, we can set up an equation using the formula: distance = speed × time.
Let's denote the time elapsed by T, and the distance traveled by locomotive A as D(A) and locomotive B as D(B) before they meet.
Since locomotive A starts 15 kilometers ahead of locomotive B, it means that D(A) = D(B) + 15.
The equation for locomotive A is: D(A) = 100T.
The equation for locomotive B is: D(B) = 140T. Note that both locomotives are traveling at their respective speeds for the same amount of time.
Now, substitute D(B) from the equation for locomotive B into the equation for D(A):
D(A) = D(B) + 15
100T = 140T + 15
Rearrange the equation to isolate T:
100T - 140T = 15
-40T = 15
T = -15/40
T = -0.375 (negative because it means they traveled in opposite directions)
Since time cannot be negative in this context, we know that they have not yet met.
To find out how far each traveled before they meet, we can substitute the value of T into the equations for D(A) and D(B):
D(A) = 100T = 100 * -0.375 = -37.5 km
D(B) = 140T = 140 * -0.375 = -52.5 km
Again, the negative distances indicate that they haven't met yet.