Bill started west on road U.S. 50, riding a bicycle at an average rate of 9 mph. Four hours later Charles started after Bill on a motor cycle and overtook him in 2 hours. What was Charles' rate? Which equation could be used to solve for Charles' rate if it is represented by x?

Question

Bill started west on road U.S. 50, riding a bicycle at an average rate of 9 mph. Four hours later Charles started after Bill on a motor cycle and overtook him in 2 hours. What was Charles' rate?  Which equation could be used to solve for Charles' rate if it is represented by x?

ddcamp · Answer

How long (total) has Bill been travelling when Charles overtakes him?
Use that time to find the distance that Charles traveled in two hours.

phi · Answer

You should know
rate * time = distance   
(or speed* time= distance   or velocity * time=distance.... they all mean the same thing)

they say
Charles' rate if it is represented by x

so replace rate with x:

x * time= distance


next, read this
Charles started after Bill on a motor cycle and overtook him in 2 hours.

that means Charles was driving for 2 hours.  His time is 2 hours.  replace time with 2:

x*2 = distance   or
2x = distance

now you need to find the distance Charles traveled.   It will be the same distance that Bill traveled,  going at 9 mph  for 6 hours