Algebra 2 story problem. Help anyone?

Question

Two motorcycles, heading towards each other on a divided highway, are 392 miles apart. If one is traveling at 52 mph and the other is 8 mph faster, in how many hours will they pass each other? Help me please

Answer 1

The first and simplest step is to determine the actual speed of the second motorcycle:  8 mph faster than 52 mph is, of course, 60 mph.

 

Then, consider how fast they're moving relative to one another.  Since the problem says that they are heading towards each other, the speed of each motorcycle adds together to determine the speed of this approach.  (You may think of this as how quickly one motorcycle "sees" the other coming at it).  52 mph + 60 mph = 112 mph.

 

Once you have this, it's just a matter of using the formula relating time, speed, and distance

distance = speed * time

 

Or, equivalently,

time = distance / speed

 

Which in this case is time = 392 miles / 112 mph = 3.5 hours.