distance traveled to work

Question

when Wayne Pourciau drives his car to work, the trip takes 30 minutes. when he rides the bus, it takes 45 minutes. the average speed of the bus is 12 miles per hour less than his speed when driving. find the distance he travels to work.

Answer 1

Let the we denote the distance traveled by d,

average speed of the car v_c,

and the average speed of the bus v_b.

 

We use the relationship

distance = speed (times) time

for the bus and the car.

 

d = 30/60 • v_{c             (1)}

d = 45/60 • v_{b             (2)}

 

We also know the relationship between the two average speeds v_c and v_b:

v_b = v_c -12.                (3)

 

We will substitute the value of bus speed in (2) and then we subtract equation (2) from equation (1):

    d =45/60 • (v_c-12)

-

    d =30/60 • v_c

    0 = 45/60 v_c -45/60 •12 -30/60 v_c

    15/60 v_c - 9=0.

 

We solve that equation and find v_c (calculation omitted):

v_c = 36.

 

Next, we use the equation (1) to find the distance:

 

d = 30/60 • 36 m/h

d =18 miles.

 

Questions?

 

For your understanding, you may change the numbers and try to write and solve the problem again.