Question

Two cars left the city for a suburb, 120 km away, at the same time. The speed of one of the cars was 20 km/hour greater than the speed of the other, and that is why it arrived at the suburb 1 hour before the other car. Find the speeds of both cars.

Answer 1

Answer:

V1 = 60 km/h

V2 = 40 Km/h

Step-by-step explanation:

The speed of an object is defined as

Speed =  distance / time

Let

V1 be the speed of the faster car

V2 be the speed of the other car

t1 the time it took for the first car to arrive

t2 the time it took for the second car to arrive

d1 the distance traveled by first car

d2 the distance traveled by second car

We know thanks to the problem that

V1 = V2 + 20 Km/h

t1 = t2 - 1 hour

d1 = d2 = 120 Km

d1 = V1 * t1

d2 = V2* t2

V1 * t1 = V2* t2

V1* t1 = (V1 -20)*(t1 +1)

The system of equations

(V1 -20)*(t1 +1) = 120

V1 * t1 = 120

120 + (120/t1) -20*t1 = 140

(120/t1) -20*t1  = 20

Which gives,

t1 = 2

This means

V1 = 60 km/h

V2 = V1 - 20 Km/h =  40 Km/h