Word probs: finding speeds; finding working times

[klubbhead024]

I had a couple questions here. I don't need the problem solved, just the equations so I can solve them. Thanks

1. Jack's workout consists of jogging for 3 miles and then biking for 5 miles at a speed 4mph faster then he jogs. If the total workout time is 1 hour, find his jogging speed and his hiking speed

2. Together Karen and Tom can clean their whole house in 3 hours. Alone Karen can clean house one hour faster then Tom can alone. About how long does it take Karen working alone to clean the house?

 

[soroban]

Re: Word problem help

Hello, klubbhead024!

1. Jack's workout consists of jogging for 3 miles and then biking for 5 miles
at a speed 4mph faster then he jogs. .If the total workout time is 1 hour,
find his jogging speed and his biking speed.

We will use: \(\displaystyle \text{Distance}\:=\:\text{Speed}\,\times\,\text{Time}\;\;\Rightarrow\;\;T \:=\:\frac{D}{S}\)

Let \(\displaystyle x\) = jogging speed.
Then \(\displaystyle x+4\) = biking speed.

He jogs 3 miles at \(\displaystyle x\) mph. .This takes him: \(\displaystyle \L\frac{3}{x}\) hours.

He bikes 5 miles at \(\displaystyle x+4\) mph. .This takes him: \(\displaystyle \L\frac{5}{x+4}\) hours.

His total workout time is 1 hour . . . There is our equation!

. . \(\displaystyle \L\frac{3}{x}\,+\,\frac{5}{x+4}\;=\;1\)

2. Together Karen and Tom can clean their whole house in 3 hours.
Alone Karen can clean house one hour faster then Tom can alone.
About how long does it take Karen working alone to clean the house?

Here's my approach to "Work" problems.
. . I break it down to the amount of work done in one hour.

Together, they do the job in 3 hours.
. . In one hour, they complete \(\displaystyle \frac{1}{3}\) of the job. .[1]

Let \(\displaystyle x\) = number of hours for Karen to do the job alone.
In one hour, Karen can do \(\displaystyle \L\frac{1}{x}\) of the job.

Since Tom takes one hour more than Karen,
. . then \(\displaystyle x+1\) = number of hours for Tom to do the job alone.
In one hour, Tom can do \(\displaystyle \L\frac{1}{x+1}\) of the job.
Together, in one hour, they can do: \(\displaystyle \L\,\frac{1}{x}\,+\,\frac{1}{x+1}\) of the job. .[2]


[1] and [2] represent the same quantity . . . There is our equation!

. . . \(\displaystyle \L\frac{1}{x}\,+\,\frac{1}{x+1}\;=\;\frac{1}{3}\)

 

[klubbhead024]

ok... I was wrong... I still need help solving it

 

[stapel]

ok... I was wrong... I still need help solving it

Are you saying that your class hasn't yet covered how to solve rational equations, so you're needing lessons...?

Thank you.

Eliz.