Word problem

Question

Two cars leave towns 1000 kilometers apart at the same time and travel toward each other. One car's rate is 20 kilometers per hour more than the other's. If they meet in 5 hours, what is the rate of the faster car?

Answer 1

D = total distance both cars cover

t = time passed from starting point to when the cars meet

V_a=the speed of the slower car

V_b=the speed of the faster car

D_A=the distance travelled by the slower car.

D_B=the distance travelled by the faster car.

 

The sum of the distances travelled by each car equals the total distance between the two starting points.

D = D_A + D_B

 

The distance travelled for each car is the speed multiplied by the time elapsed.

 

D_A = V_At

D_B = V_Bt

 

From the problem we know, V_B = V_A + 20

 

Putting all of this together,

 

D = V_At + (V_A + 20)t,

 

D/t = 2V_A + 20

 

V_A = D/2t - 10

 

plugging in all the values: V_A = 90km/hr.

 

the faster automobile travels at V_B = 110km/hr.

Answer 2

Assume that the rate of the faster car is m miles per hour. Then the other car travels m-20 kilometers per hour, so after 5 hours the faster car has traveled 5m kilometers and the other car 5(m-20). These two should sum to 1000, so

5m+5(m-20)=1000

10m-100=1000

10m=900

m=90

Answer 3

d = r · t

 

5r + 5(r + 20) = 1000

5r + 5r + 100 = 1000

 

Can you solve for r?