two locomotives start at the SAME place but Locomotive A gets a half hour head start. Locomotive A travels at 100 km/hr and Locomotive B travels at 140 km/hr.Find the time elapsed and how far each traveled before they meet.
v(A) • (t+0.5) =v(B) •t
0.5•v(A) = (v(B) –v(A)) •t
t= 0.5•v(A) /(v(B) –v(A)) =
=0.5•100/40=1.25 h
s=v(B) •t=140•1.25=175 km
To find the time elapsed and how far each locomotive traveled before they meet, we first need to determine when they will meet.
Let's assume that the time elapsed when they meet is 't' hours. Since Locomotive A has a half-hour head start, it will travel for 't + 0.5' hours, while Locomotive B will only travel for 't' hours.
The distance traveled by Locomotive A can be calculated using the formula: distance = speed × time. In this case, Locomotive A travels at 100 km/hr for 't + 0.5' hours, so its distance traveled is 100 × (t + 0.5) km.
Similarly, the distance traveled by Locomotive B is 140 × t km.
Since they meet at the same place, their distances will be equal when they meet. Therefore, we can set up an equation:
100 × (t + 0.5) = 140 × t
Now, let's solve this equation to find the value of 't', which will give us the time elapsed when they meet.
100t + 50 = 140t
50 = 40t
t = 50/40 = 1.25
Therefore, it will take 1.25 hours for the two locomotives to meet.
Now, we can calculate the distance each locomotive traveled before they meet.
Distance traveled by Locomotive A = 100 × (1.25 + 0.5) = 100 × 1.75 = 175 km.
Distance traveled by Locomotive B = 140 × 1.25 = 175 km.
So, each locomotive will travel a distance of 175 km before they meet, and it will take them 1.25 hours to meet.