loren drove 200 miles at a certain rate, and his wife, lois, drove 100 miles at a rate 10 mph slower. if loren had driven for the entire trip, they would have arrived 30 minutes sooner. what was loren's rate?

As long as Loren drove, the law of motion was

As long as Loid drove, the law of motion was

So, the total time they took is

Had Loren driven the whole time, the law of motion would have been

And we know that this time would have been 30 minutes (i.e. 0.5 hours) faster. So, we have

This translates into

If we subtract 200/s from both sides, we have

We can simplify the right hand side by summing the two fractions:

So, we have to solve

If we cross multiply the denominators, we have

Which yields the solutions

We accept the positive solution, because the negative would mean to travel backwards, so Loren's rate was 50mph

the answer is 99.

8987678

step-by-step explanation: