1. ## Word Problem

At 8:00 AM a train leaves Topeka for Santa Fe and another train leaves Santa Fe for Topeka. The trains maintain constant speeds with no stops. The first train requires 5 hours to complete the trip, and the second train requires 7 hours. At what time do the trains pass each other?

2. Originally Posted by bearej50
At 8:00 AM a train leaves Topeka for Santa Fe and another train leaves Santa Fe for Topeka. The trains maintain constant speeds with no stops. The first train requires 5 hours to complete the trip, and the second train requires 7 hours. At what time do the trains pass each other?
one train travels at the rate of $d$ miles in 5 hrs

the other train travels at a rate of $d$ miles in 7 hrs

let $t$ = time in hours when they meet

$\frac{d}{5} \cdot t + \frac{d}{7} \cdot t = d$

solve for $t$