SOLUTION: A car and a truck leave the same place at the same time. the car is traveling twice as fast as the truck. In three hours time, the car is ahead of the truck by 72 miles. at what ra

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A car and a truck leave the same place at the same time. the car is traveling twice as fast as the truck. In three hours time, the car is ahead of the truck by 72 miles. at what ra      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 231990: A car and a truck leave the same place at the same time. the car is traveling twice as fast as the truck. In three hours time, the car is ahead of the truck by 72 miles. at what rate of speed is each vehicle driving?
Found 2 solutions by drj, josmiceli:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A car and a truck leave the same place at the same time. The car is traveling twice as fast as the truck. In three hours time, the car is ahead of the truck by 72 miles. at what rate of speed is each vehicle driving?

Step 1. Let x be the speed of the truck.

Step 2. Let 2x be the speed of the car since it is traveling twice as fast as the truck.

Step 3. Distance= speed * time.

Step 4. Let 3x be the distance traveled by the truck after 3 hours

Step 5. Let 3*2x=6x be the distance traveled by the car after 3 hours.

Step 6. Using Steps 4 and 5, then, 6x-3x=72 since they are 72 miles apart after 3 hours.

Step 7. Solving leads to 3x=72 or 3x%2F3=72%2F3=24 or x=24 miles per hour. Then 2x=48 miles per hour.

Step 8. ANSWER. The truck is 24 miles per hour and the car is 48 miles per hour.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In this problem, both the car and the truck are traveling
for the same amount of time.
Write separate d+=+r%2At equations for both
given:
t is the same for both
d%5Bc%5D+=+d%5Bt%5D+%2B+72
r%5Bc%5D+=+2%2Ar%5Bt%5D
----------------------------
(1) d%5Bc%5D+=+r%5Bc%5D%2At
(2) d%5Bt%5D+=+r%5Bt%5D%2At
and, rewriting:
(1) d%5Bc%5D+=+r%5Bc%5D%2At
(2) d%5Bc%5D+-+72+=+%28r%5Bc%5D%2F2%29%2At
--------------------------------
Multiply both sides of (2) by 2
(2) 2d%5Bc%5D+-+144+=+r%5Bc%5D%2At
Now substitute (1) in (2)
(2) 2d%5Bc%5D+-+144+=+d%5Bc%5D
Subtract d%5Bc%5D from both sides
(2) d%5Bc%5D+=+144 mi
and from
d%5Bc%5D+=+d%5Bt%5D+%2B+72
d%5Bt%5D+=+d%5Bc%5D+-+72
d%5Bt%5D+=+144+-+72
d%5Bt%5D+=+72
They both travelled for 3 hrs, so
The car's speed is
144%2F3+=+48 mi/hr
The truck's speed is
72%2F3+=+24 mi/hr