Algebra help

Question

The smith family drove to their vacation home in Michigan in 5 hours. The trip home took only 3 hours since they averaged 26 mph more due to light traffic. How fast did they drive each way?

Answer 1

The first step in any word problem is to turn the words into equations that we can work with.

 

We know that the first drive took 5 hours, but we don't know the distance nor their speed. We also know that distance = rate * time. We know that D is the same for both drives.

 

So we have this:

 

D = R * 5 (where R is their rate of speed on the first drive)

 

We know that the second drive took 3 hours and their rate was 26mph faster than before, so we have this:

 

D = R2 * 3

D = (R + 26) * 3

D = 3R + 78

 

We now have two equations and two variables, so we can solve for R.

 

3R + 78 = 5R

78 = 2R

R = 39 mph

 

Therefore they drove 39mph on the first trip and they drove 65 mph on the second.