word problem motion resubmitted

Question

Two automobiles, A and B leave at same time and travel same route. Automobile A goes a rate of 55 miles per hour. Automobile B goes a rate of 40 miles per hour. How many hours after they begin the trip, will A be 60 mi ahead of B?

Answer 1

Let's assume they start from the same position, so when they start, A is 0 miles ahead of B.  We'll use t as the time variable, and say when they start, t = 0.

 

We can convert their velocities into distances.  Since velocity = distance/time, distance = velocity * time.  The question gives velocities in units of miles/hour, and the answer is to be given using these units, so no conversions are necessary.

 

We'll call A the distance traveled by car A in t hours, and B the distance traveled by car B in t hours.

A = 55*t

B = 40*t.

 

Since A and B are distances, the distance between the cars is A - B.  The question asks us to find t when the distance between the cars is 60 mi, or

A - B = 60.

 

Substituting in our formulas for A and B allows us to find t:

 

55t -40t = 60.  Subtract:

15t = 60.  Divide both sides by 15.

t = 4 hours.