Problem Solving (Speed/Distance)?

Initially, I am (25 + 25) m = 50 m behind the front of the truck, as the truck is 25 m long.
When there is a gap 50 m between me and the truck, I am 50 m in front of the front of the truck.
I need driving (50 + 50) m = 100 m = 0.1 km more than the truck.

In each hour, I drive (120 - 100) km = 20 km more than the truck.
Time taken to drive 0.1 km more than truck = (0.1 km) / (20 km/h) = 0.005 h

Distance I traveled = (120 km/h) × (0.005 h) = 0.6 km
Distance from the junction after I drive 0.6 km = (2 - 0.6) km = 1.4 km

To simplify the situation, it's like the truck is stopped, and you' at a speed of 20 km/h.

To be in front of the truck, and safe, you must perform:

- 25 m to get to the truck (this is the distance between you and the truck)

- 25 m to overtake the truck (this is the length of the truck)

- 50 m to complete the safe distance

You must therefore make 100 m, considering that the truck is stationary.


You are travelling at 20 km/h, because the truck is stopped. Recall the speed:

s = d/t → where s is the speed, d is the distance, t is the time

t = d/s → we've just seen that: s = 20 km/h

t = d/20 → you know that the distance is 100 m, i.e. 0.1 km

t = 0.1/20

t = 0.005 h ← this is the necessary time (in hour) to make 100 m → recall: 1 h = 3600 s

t = 0.005 * 3600

t = 18 s ← this is the necessary time (in second) to make 100 m


But, your real speed is 120 km/h. How far had you been in 18 seconds?

120 km in 1 hour

120 km in 3600 s

x km in 18 s


You make the cross multiply, and you obtain:

x * 3600 = 120 * 18

x = (120 * 18)/3600

x = 0.6 km ← this is the distance you made after 18 s


When you decide to overtake the truck, the distance from the junction is 2 km.

Now, the distance between you and the junction is:

= 2 - 0.6

= 1.4 km

Start by sketching a diagram...