Question

A tourist was planning a trip by car for traveling at some constant speed for 2.5 hours. However, he found that if he increases the speed by 20 km/h he can cover the same distance in 30 minutes less time than it was planned. What was the planned speed of the tourist, in km/h?

Answer 1

The expected speed is 80 km / h

Explanation:

To solve this problem we must propose two equations that relate the data provided in the statement.

Initially it was expected to travel for 2.5 hours.

If we call V the speed at which the car would travel during that time and we also call x the distance traveled then we propose the following equation:

`2.5V = x` (i)

Then we know that if V increases 20 km/h then t decreases in 0.5 hours:

`V + 20 = (x)/((2.5-0.5))` (ii) *We know that V = x/t

Then we substitute (i) in (ii)

`V + 20 = (2.5V)/(2)\\\\(5)/(4)V - V = 20\\\\(1)/(4)V = 20\\\\V = 20(4)\\\\V = 80`

The expected speed is 80 km/h

and the distance to be covered is 200 km