QUESTION ABOUT CARS MOVING

Question

Two cars are traveling down the highway with the same speed. If the first car increases its speed by 1km/hr, and the other car decreases its speed by 10km/hr, then the first car will cover the same distance in 2hrs as the second car in 3hrs. What is the speed of the cars?

Two cars are traveling down the highway with the same speed. If the first car increases its speed by 1km/hr, and the other car decreases its speed by 10km/hr, then the first car will cover the same distance in 2hrs as the second car in 3hrs. What is the speed of the cars?

Answer 1

Let x = original speed of the cars

 

Distance = (Rate)(Time)

 

Distance of first car = 2(x+1)

 

Distance of second car = 3(x-10)

 

2(x+1) = 3(x-10)

 

2x+2 = 3x-30

 

     x = 32 km/hr

 

Answer 2

Hi Nik,

 

Remember that distance = rate * time  or distance = speed * time.  Both are covering the same distance so the distance of car A = speed of car A * 2 hours.  The distance of car B = speed of car B * 3 hours.   

 

If s= the original speed of both cars, then the speed of car A = s + 1   and the speed of car B = s - 10.

 

Putting these into the distance we get

 

Dist of car A = (s+1)*2     Dist of car B = (s-10)*3

 

Since the distances are the same, Dist of car A = Dist of car B, so

 

(s+1)*2 = (s-10)*3

 

Distribute

 

2s + 2 = 3s - 30

 

Subtract 2s from both sides

 

2 = s - 30

 

Add 30 to both sides

 

32 = s

 

So the original speed was 32.  

 

Speed of car A then is 33 km/hr

Speed of car B must be 22 km/hr

 

Check to see if this works:   33*2 =66 km driven

                                          22 * 3 = 66 km driven.   correct!!!