Two cars, A and B, drives past the same line. Car A passes first with a constant speed of 65km/h. 10 seconds later car B passes with a constant speed of 70km/h. How long does it take before car B drives past car A?
+33661 Distance past line by A after time t hours = 65t km
Distance past line by B after t hours = 70*(t - 10/3600) km (10 seconds = 10/3600 hours) This assumes B is travelling at 70 km/h for the 10 seconds before passing the line.
When these are equal:
70(t - 10/3600) = 65t
70t - 700/3600 = 65t
5t = 700/3600
t = 700(3600*5) hours or t = 700/5 seconds or t = 140 seconds
+33661 Distance past line by A after time t hours = 65t km
Distance past line by B after t hours = 70*(t - 10/3600) km (10 seconds = 10/3600 hours) This assumes B is travelling at 70 km/h for the 10 seconds before passing the line.
When these are equal:
70(t - 10/3600) = 65t
70t - 700/3600 = 65t
5t = 700/3600
t = 700(3600*5) hours or t = 700/5 seconds or t = 140 seconds
+130516 65km/hr = 325/18 m/s
70km/hr = 175/9 m/s = 350/18 m/s
So in 10 sec.....the first car is 10 * 325/18 m = 3250/18 m ahead of the other when the second car reaches the line
And we need to solve this
( 350/18 - 325/18) T = 3250/18 multiply both sides by 18
[350 - 325] T = 3250
25T = 3250 divide both sides by 25
3250/25 = T = 130 seconds
Proof.......the second car closes the gap between the two vehicles by [25/18]m/s
In 130 s, the first car is 3250/18m ahead
So, in 130 s the second car makes up.....130* (25/18) = 3250/18 m and closes the gap
Car A has a head start of 10 seconds/3600 (65km/hr)
Car A position is 10/3600 (65) + 65 t
Car B position is 75 t
WHen they are equal, car B will be caught up to Car A
10/3600 (65) + 65 t = 75 t
650/3600 = 10 t
t = 65/3600 of an hour or 65 seconds
Checking: Car A Position after 65 seconds (+ 10 second head start) = 75/3600 (65km/hr) = 1.354 km from 'start line'
Car B position after 65 seconds = 65/3600 (75km/hr) = 1.354 km from 'start line'
Car A has a head start of 10 seconds/3600 (65km/hr)
Car A position is 10/3600 (65) + 65 t
Car B position is 70 t
WHen they are equal, car B will be caught up to Car A
10/3600 (65) + 65 t = 70 t
650/3600 = 5 t
t =130/3600 of an hour or 130 seconds
Checking: Car A Position after 130 seconds (+ 10 second head start) = 140/3600 (65km/hr) = 2.527 km from 'start line'
Car B position after 130 seconds = 130/3600 (70km/hr) = 2.527 km from 'start line'
SORRY.... I had wrong speed value for car B in my original submission......!
