Ms. smith spent 7 hours driving from her home to albany, a distance of 238 mi. before noon, she averaged 32 mph. after noon she averaged 39 mph. find the number of hours she traveled at each rate of speed.

ANSWER

She averaged at 32 mph for 5 hours and 39 mph for 2 hours.

EXPLANATION

Let

be the number of hours she travelled before noon and

be the number of hours she travelled after noon.

Then since she travelled for a total of 7 hours, we can write the equation,



We were also given that, before noon,she averaged at 32 mph.

We know that,



Let

be the distance before noon.


This implies that,



Also let the distance she covered after noon be,



Then,


This implies that,



Since she covered a total distance of 238 miles, we can write the equation,


This means that,



We multiply equation by 32 to get,



Equation (2) minus equation (3), will give us,



This implies that,


We substitute the value of y into equation (1) to get,







We can now conclude that she averaged at 32 mph for 5 hours and 39 mph for 2 hours.