SOLUTION: When traveling to work each day, John drives part of it on the highway (where he goes 65 mph) and the rest on a ranch road (where he can only go 42 mph). The trip is 13.95 miles, a

Algebra ->  Coordinate-system -> SOLUTION: When traveling to work each day, John drives part of it on the highway (where he goes 65 mph) and the rest on a ranch road (where he can only go 42 mph). The trip is 13.95 miles, a      Log On


   

Question 227726: When traveling to work each day, John drives part of it on the highway (where he goes 65 mph) and the rest on a ranch road (where he can only go 42 mph). The trip is 13.95 miles, and it takes only 15 minutes (which is 1/4 hour , or 0.25 hours). What part of an hour does he spend driving on each type of road?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
When traveling to work each day, John drives part of it on the highway (where he goes 65 mph) and the rest on a ranch road (where he can only go 42 mph). The trip is 13.95 miles, and it takes only 15 minutes (which is 1/4 hour , or 0.25 hours). What part of an hour does he spend driving on each type of road?

Step 1. Let t be the time (in hours) traveled on the highway.

Step 2. Let 65t be the distance traveled on the highway.

Step 3. Let 0.25-t be the time traveled (in hours) on the ranch road.

Step 4. Let 42(.25-t) be the distance traveled on the ranch road.

Step 5. Then 13.95=65t+42(0.25-t)=10.5+23t since the total distance is 13.95 miles.

Step 6. Solving yields the following steps

13.95=10.5%2B23t

Subtract 10.5 from both sides of the equation

13.95-10.5=10.5%2B23t-10.5

3.45=23t

Divide by 23 to both sides of the equation

3.45%2F23=23t%2F23

t=0.15 hour and 0.25-t=0.10 hour

Check distance traveled 65*0.15+42*0.10=9.75+4.2=13.95 which is a true statement.

Step 7. ANSWER: John spent 0.15 hour on the highway and 0.10 hour on the ranch road.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV