SOLUTION: A person rides his bike to the park at 12 miles per hour then back home at 16 miles per hour. If the total trip took 7 hours how far was the park?

Question 228500: A person rides his bike to the park at 12 miles per hour then back home at 16 miles per hour. If the total trip took 7 hours how far was the park?
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
A person rides his bike to the park at 12 miles per hour then back home at 16 miles per hour. If the total trip took 7 hours how far was the park?

Step 1. distance=speed * time.

Step 2. Let x be the amount of time it takes to get to the park.

Step 3. Let 7-x be the amount of time going home from the park since it took 7 hours total for the whole trip.

Step 4. Let 12x be the distance to the park at 12 miles per hor.

Step 5. Let 16(7-x) be the distance going back to home at 16 miles per hour.

Step 6. But the distances in Steps 4 and 5 are equal. Then, 12x=16(7-x).

Step 7. Solving yields the following steps

Add 16x to both sides to get x-terms on the left side of the equation

Divide by 28 to both sides of the equation

hours.

Step 8. Then, distance to park is 12x=48 miles. Check if same when going back home or 16(7-x)=16*3=48 miles as well.

Step 9. ANSWER; Solution is 48 miles between the park and the person's home.

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.

Good luck in your studies!

Respectfully,
Dr J
RELATED QUESTIONS
Mr. Johnson rode his bike from his house to a store in Woodland Park at a rate of 10.3... (answered by stanbon)

sally walked(4miles per hour) frome home to the bike shop. She then rode her newly... (answered by checkley77)

Rosie ran to the park at 7 miles per hour and walked back home at 3 miles per hour. How... (answered by math_tutor2020,josgarithmetic,Alan3354)

Jim rides his bike to school every morning at an average speed of 15 miles per hour. He... (answered by mananth)

Richie put on his jogging shoes and speed-walked to the park at 5 miles per hour. Then he (answered by checkley75)

A man rides a bike a straight distance at a speed of 10 miles per hour. He came back the... (answered by ankor@dixie-net.com)

the cross-country team left school and trotted at 6 miles per hour. then they ran back to (answered by Earlsdon)

John began a 164mile bicycle trip to build up stamina for a triathlon competition.... (answered by ankor@dixie-net.com)

Sam rode his bike for 1 mile to a friend's house. Then his friend's mom drove him 12... (answered by ankor@dixie-net.com)