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

Answer:

The expected speed is 80 km / h

Step-by-step 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:

$V + 20 = \frac{x}{(2.5-0.5)}$ (ii)             *We know that V = x/t

Then we substitute (i) in (ii)

$V + 20 = \frac{2.5V}{2}\\\\\frac{5}{4}V - V = 20\\\\\frac{1}{4}V = 20\\\\V = 20(4)\\\\V = 80$

The expected speed is 80 km/h

and the distance to be covered is 200 km