Final answer:
The initial speed of the vehicle was 60 km/h, which is determined by setting up an equation relating the initial speed, increased speed, time difference, and distance traveled.
Step-by-step explanation:
The initial speed of a vehicle that traveled a distance of 120 km. The time taken was reduced by 30 minutes when the speed was increased by 20 km/h. Let's denote the initial speed as v km/h and the reduced time as t - 0.5 hours (since 30 minutes is 0.5 hours). The time taken at the initial speed is 120/v hours, and the time at the increased speed is 120/(v+20) hours. Using the information given, we set up the following equation:
120/v - 120/(v + 20) = 0.5
Upon solving this equation for v, we find that the initial speed was 60 km/h.