Question

Two trains leave towns 1016 kilometers apart at the same time and travel toward each other. One train travels 10 km/ h faster than the other. If they meet in 4 hours, what is the rate of each train?

Answer 1

Using the given information, we can set the following system of equations:

$\begin{gathered} 4r_1+4r_2=1016, \\ r_2=r_1+10, \end{gathered}$

where r₁, and r₂ are the rates of the trains.

Substituting the second equation in the first one, we get:

$4r_1+4(r_1+10)=1016.$

Solving for r₁, we get:

$\begin{gathered} 4r_1+4r_1+40=1016, \\ 8r_1+40=1016, \\ 8r_1=1016-40, \\ 8r_1=976, \\ r_1=\frac{976}{8}, \\ r_1=122. \end{gathered}$

Therefore:

$r_2=122+10=132.$

Answer:

$\begin{gathered} 122\text{ km/h,} \\ 132\text{ km/h.} \end{gathered}$