word problem

Question

Two automobiles leave the same city simultaneously and both head towards another city. The speed of one is 10 km/hour greater than the speed of the other, and this is why the first automobile arrives at the destination 1 hour before the other. Find the speed of both automobiles knowing that the distance between the two cities is 560 km.

Two automobiles leave the same city simultaneously and both head towards another city. The speed of one is 10 km/hour greater than the speed of the other, and this is why the first automobile arrives at the destination 1 hour before the other. Find the speed of both automobiles knowing that the distance between the two cities is 560 km.

Answer 1

Use the formula distance = rate x time

 

Automobile 1 has a rate of x

Automobile 2 has a rate of x + 10

 

Automobile 1 makes the trip in t hours

Automobile 2 makes the trip in t - 1 hours

 

We have two equations, remembering that the distance traveled is the same for each auto

 

560 = xt

560 = (x + 10)(t - 1)

 

Use the Substitution Method and solve the first equation for t.

t = 560/x

 

Plug this value of t into the second equation

 

560 = (x + 10)(560/x - 1)

560 = 560 - x + 5600/x - 10

560 = 550 - x + 5600/x

560x = 550x - x² + 5600

x² + 10x - 5600 = 0

(x - 70)(x + 80) = 0

 

The only logical solution is x = 70

 

Automobile 1 has a speed of 70 km/h

Automobile 2 has a speed of 80 km/h