Two cars started from the same point at 5 a.m. traveling in opposite directions at 40 and 50 mph respectively. At what time will they be 450 miles apart?

Question

solve a distance word problem

Answer 1

d = vt

 

When moving in opposite directions, add the 2 speeds.

 

v = (40 + 50) mph = 90 mph

 

d = 450 mi

 

t = d/v = 450/90 h = 5 h

 

They will be 450 miles apart 5 hours after 5:00 am, which puts you at 10:00 am.

Answer 2

So in 1 hour, let's say the first car travels 40 miles to the left (-40, 0), and the second car travels 50 miles to the right (50, 0). 

Their distance is |-40 - 50| = 90 miles apart.

In the 2 hours, the first car is at (-80, 0) and the second car is at (100, 0).

Their distance is |-80 - 100| = 180 miles apart, or simply 90 × 2.....

 

If you can see this pattern above, hopefully you also spot that 450 is divisible by 90, so we'll get a whole number of hours.

450 ÷ 90 = 5 hours from the beginning time that they would have to drive to be that far apart.

Lastly, just add the 5 hours to 5am to get the answer of 10am

Hope this helps!