Fred made the trip by car in 20 hours and the return trip by bus in 16 hours. How long was the drive if the bus traveled 10 mph faster than the car ?

Question

can you show me how to work it out and what the answer is 

Answer 1

Hi Stephen,

 

Let's begin by writing the distance formula:

    distance (d) = rate (r) x time (t)

 

Since the distance traveled by car and by bus is the same, we can write this equation to solve for the rate (r) of the car:

    20r = 16(r + 10)  [car distance = bus distance]

    20r = 16r + 160

    20r - 16r = 160

    4r = 160

      r = 160/4

      r = 40 mph

 

Now we can plug in our value for r back into our equation and evaluate each side of the equation to calculate the same distance that was traveled by car and by bus:

    20r = 16(r + 10)

    20(40) = 16(40 + 10)

    800 = 16(50)

    800 = 800

 

Thus, the distance traveled is 800 miles.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

distance=rate*time

d=r*t

d=r*20 for the car

d=(r+10)*16 for the bus

equate the two right sides because they are both equal to d

20r=16(r+10)

20r=16r+160

20r-16r=160

4r=160

r=160/4

r=40 mph for the car

r+10=50 mph for the bus

distance=40*20=800 miles or distance=50*16=800 miles

the drive or total distance is 800+800=1600 miles