Word Problem

[pagethru]

I am trying to figure out this word problem but am very confused. Any help would be greatly appreciated!!

"Mark can overhaul an engine in 20 hours and Phil can do the same job by himself in 30 hours. If they both work together for a time and then Mark finishes the job himself in 3 hours, how long did they work together?"

 

[tkhunny]

The usual question would be, "How long working together?"

1/20 + 1/30 = 5/60 = 1/12 ==> 12 Hours

This gives the rate for working together.

"For a time" needs a name. How about 't', in hours?

(1/12)*t + (1/20)*3 = ??

Now what?

 

[soroban]

Hello, pagethru!

Here's my approach . . . it's different. $\displaystyle \;$ (Is anyone surprised?)

Mark can overhaul an engine in 20 hours and Phil can do the same job by himself in 30 hours.
If they both work together for a time and then Mark finishes the job himself in 3 hours,
how long did they work together?

Let $\displaystyle x$ = number of hours they worked together.

Mark can do the job in 20 hours.
$\displaystyle \;\;$In one hour, he can do $\displaystyle \frac{1}{20}$ of the job.
$\displaystyle \;\;$in $\displaystyle x$ hours, he can do $\displaystyle \frac{x}{20}$ of the job.

Phil can do the job in 30 hours.
$\displaystyle \;\;$In one hour, he can do $\displaystyle \frac{1}{30}$ of the job.
$\displaystyle \;\;$In $\displaystyle x$ hours, he can do $\displaystyle \frac{x}{30}$ of the job.

Together, in $\displaystyle x$ hours, they did $\displaystyle \,\frac{x}{20}\,+\,\frac{x}{30}$ of the job.
Then Mark worked alone for 3 hours; he did $\displaystyle \frac{3}{20}$ of the job alone.

The sum of this work is one (1) job: $\displaystyle \:\frac{x}{20}\,+\,\frac{x}{30}\,+\,\frac{3}{20}\;=\;1\;$ . . . there!

 

[tkhunny]

it's different.

hardly. I just glued them together first.