Bicycle rider (rate, distance, time question)

[Femme_physics]

1. The problem statement, all variables and given/known data

A bicycle rider rides from town A to town B on a paved road in a constant speed of 20 km/h. On his way back he rides in a constant speed on a bypassing road that's 25% longer than the paved road. The speed of the bicycle rider in the bypassing road is 5 km/h slower than his speed on the paved road. The riding time of the rider in the bypassing road was 2 hours longer than his time riding on the paved road.

Find the length of the paved road from town A to B, and the bypassing road from A to B.


2. Relevant equations

D = RT

3. The attempt at a solution

Attached

[eumyang]

First, in your table, switch the column labels "T" and "R". 20 & 15 are the speeds, and x & x + 2 are the times.

Second, your expression for D in the 2nd ride is wrong. Remember, the distance of the bypass is 25% longer than the paved road. The expression you wrote is a distance that is 25% longer than the bypass. So the expression should be
1.25(20x) = 25x

Your equation, therefore, should be the D=RT equation for the return trip, or
\begin{aligned}
D &= RT \\
25x &= 15(x + 2)
\end{aligned}

[Femme_physics]

You're great, eumyang, thank you very much :)

[Femme_physics]

It was rather challenging for me to solve it since I'm used to equate riders distances to each and that normally gets me X. In here we had to artificially manipulate the distance based on the text info and well... just use D = RT. It's rather brilliant in its simplicity now that I think about it.

Anyway, thanks again :)