story problems

Question

Collins left his house and rode his bike into town 8 mph. along the way he got a flat tire so he had to turn around and walk his bike back to his house traveling 4 mph if the trip down and back took 12 hours, how far did he get before his tire went flat? 

Answer 1

distance=rate*time

d=rt

d=8t into town

d=4(12-t) back home

8t=4(12-t) because they are both equal to d

8t=48-4t

8t+4t=48

12t=48

t=48/12

t=4 hours

d=8*4

d=32 miles before his tire went flat

Answer 2

Hi Sandra--

 

So he bikes at twice the speed he walks. And since the distance down is the same as the distance back, the trip back had to take him twice as much time.

 

Since the round trip was 12 hours, you need trip N + trip 2N to equal 12. 3N = 12, so N = 4 hours down, and 2N = 8 hours back.

 

Knowing that, you can say that if he traveled down for 4 hours at 8 miles per hour, he traveled 32 miles before he broke down and had to hike back the same 32 miles, which took him 8 hours at 4 miles per hour, for a total of 64 miles in 12 hours. (Average speed 5.33 miles per hour, I think...)

 

Which proves two things:

 

This boy is a very slow biker. And he's a wicked fast walker! :-)

 

Hope this helps!

 

Matt in New York