Help with an algebra question?

It took betty 1.8 hrs to drive to her mother's house on Sat morning. On her return trip on Sun night, traffic was heavier, so her trip took her 2 hrs. Her average speed on Sun was 5 mph slower than Sat. What was her average speed on Sun.


First you have to figure out the distance she traveled. On Saturday, the distance x took her 1.8 hours to drive, on Sunday the same distance x took her 2 hours to drive. We know that when you take the distance (x) and divide by the time needed to travel (1.8 and 2 hours) you will get the speed she traveled. We also know that the difference between her speed on sat vs sunday was 5 mph.

So you can set up the equation like so.

(x/1.8) - (x/2) = 5. This means that the speed on Saturday (x/1.8) minus the speed on Sunday (x/2) is 5 mph.

Now to solve for x. Find the common denominator, just multiply 1.8 and 2 which is 3.6. So the equation becomes:

(2x/3.6) - (1.8x/3.6) = 5 With a common denominator, subtraction becomes simple. So the equation becomes:

0.2x/3.6 = 5 To solve for x, multiply both sides by 3.6. the equation becomes:

0.2x=18. Divide both sides by 0.2, so then x = 90.

Now the x we said represents the Distance traveled. So she traveled 90 miles. On saturday her speed was 90/1.8 which is 50 mph, on sunday her speed was 90/2 which is 45 mph. 50 and 45 are 5 apart just as the question asked. So you can now confirm that she traveled 45 mph on sunday.