A bus traveling 40mi/h amd a car traveling 50mi/h cover the same distance. The bus travels 1 hr more then the car. How many hours did each travel?

Question

Find the equation and then the answer?

Answer 1

Hi Dawn, the solution to this problem uses the D(istance) = R(ate) * T(ime) equation. The best way to solve the problem is to set up a table.

 

Let x represent the unknown time.

 

Vehicle          Distance           Rate          Time

----------------------------------------------------

Bus                    *                 40               x + 1

 

Car                    *                 50                 x

 

Since the distance traveled by the bus and car is the same, the bus distance equals the car distance.

 

Car distance:

 

D_c = R_c * T_c

 

D_c = 50 * x

 

Bus distance:

 

D_b = R_b * T_b

 

D_b = 40 * (x + 1)

 

Solve:

 

D_b = D_c

 

40 * (x + 1) = 50 * x

 

Solve for x:

 

40x + 40 = 50x

 

Combine terms:

 

10x = 40

 

x = 4

 

The car took 4 hours to cover the distance.

 

The bus took 4 + 1, or 5 hours to cover the distance.

 

Check:

 

D_b = D_c

 

40 * ( 4 + 1) = 50 * 4

 

40 * 5 = 50 * 4

 

200 = 200

 

Values check.

 

Questions?