linear equation word problem II

[Karrie1113]

bicyclist and jogger leave the gym at the same time. Bicyclist rides 6mph faster than the jogger. it takes the jogger 2 hr to complete the same distance as the bicyclist in 1 hour. find the speed of each person.

Here are my thoughts
rate*Time=Distance
RIDER
Rate=R+6
time =1 hr
distance is 1(R+6)

JOGGER
rate=R
time =2 hr
distance = 2(R)

Equation 1(R+6)=2(r)
1R+6=2R
subtract 6 from both sides
1R=2R-6
subtract 2R from both sides
-R=-6
R=6

Is this correct?

 

[mmm4444bot]

Equation 1(R+6)=2(r) ? This is good, except don't change R to r. Use R throughout.

Also, it's standard to not explicitly write coefficients of 1.

In other words, 1(R + 6) is written as (R + 6), and the coefficient 1 is understood to be there.

Same with 1R. We write R instead, and it's understood that this means 1R.



1R+6=2R
subtract 6 from both sides
1R=2R-6
subtract 2R from both sides
-R=-6
R=6

Is this correct?

Yes, so far.

What is the meaning of the value 6 for R ?

Can you answer the given question now ?

 

[mmm4444bot]

For your information only, here's another way to solve the same equation.

R + 6 = 2R

Subtract R from both sides

6 = R