How do I solve this problem?

Question

Clark Kent Made the trip by bus in 16 hours and the return trip by car in 20 hours. The bus traveled 10 miles per hour faster than the car. How far was the trip?

Answer 1

Let c be the speed of the car. Let b be the speed of the bus.

We know that the car took 20 hours to make the trip while the bus took only 16. (20c = 16b)

Divide both sides of this equation by 4 to obtain 5c = 4b. Since the bus speed is 10 mph faster than the car, we can write the equation b = c + 10.

 

Now, replacing b with the expression c + 10, we know that 5c = 4(c +10) = 4c + 40 which means that c = 40. This means that b = 50.

 

In summary, the car traveled at a speed of 40 mph for 20 hours for a distance of 800 miles. The bus traveled for 16 hours at a spered of 50 mph which also equates to a distance of 800 miles.

 

 

Answer 2

Hi Zach,

 

This is a distance rate time problem (d=rt)

For the bus 

d = 16r  Where r is the speed of the bus

 

For the car

d = 20(r-10)   since the bus traveled 10 MPH faster than the car

 

Since the distance was the same there and back, we can set these two equations equal to one another.

 

 

16r = 20(r-10)

working through this to solve for r

 

16r = 20r - 200

200 = 4r

r = 40 

 

The bus is traveling 40 MPH and the car is traveling 30 MPH.

 

The distance is

d = 40(16) = 640 miles