# Basic algebra manipulation

• Nov 7th 2011, 11:09 AM
benny92000
Basic algebra manipulation
Problem: A baseball player travels from his home city, Jasonville, to Giambi City for a baseball game. He drives at m miles an hour. After the game, he flies home instead, traveling at p miles an hour. If the distance from jasonville to Giambi City is v miles, and it took him j hours longer to drive than to fly, what is j?

The answer is vm-vp. I set up a rate distance time chart for the first leg there and the second leg home. Then I made x+j=v/m (rate formula) and x=v/p Then I subsituted v/p for x and set j = to v/m-v/p. That was the answer I got. What did I do wrongly?
• Nov 7th 2011, 11:26 AM
FrameOfMind
Re: Basic algebra manipulation
Time taken to fly = \$\displaystyle pv\$
Time taken to drive = \$\displaystyle mv = pv + j\$

Rearrange to get;
\$\displaystyle j = mv - pv = v(m - p)\$
• Nov 7th 2011, 11:56 AM
skeeter
Re: Basic algebra manipulation
I do not agree with the given "answer", because the units do not work out. vm - vp = (distance)(speed), which is not time.

you had it correct the first time ...

rate(time) = distance

m(t+j) = v

pt = v

m(t+j) = pt

mt + mj = pt

mj = pt - mt

j = pt/m - t

j = v/m - v/p
• Nov 7th 2011, 01:18 PM
Wilmer
Re: Basic algebra manipulation
Code:

```        |....@m mph.............v miles....................>v/m hours v/p hours<................v miles................@p mph.....|```
v/m = v/p + j

j = v(p - m) / (pm)
• Nov 7th 2011, 03:06 PM
benny92000
Re: Basic algebra manipulation
It must be a typo in my book... All too common these days. Thank you for clarifying.