Question 437560
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Sarah hikes at 4 kilometers per hour from one end of a trail that is 34 km long. Amanda begins 1 hr laater at the other end. Walks toward sarah at 6 k/m. How long will it take for them to pass each other

Let time Amanda takes to meet Sarah, be T
Then, distance Amanada covers when she meets Sarah = 6T

Since Sarah started out 1 hour before Amanda, when they both meet, Sarah would've been travelling for T + 1 hours
So, distance Sarah covers when she meets Amanda = 4(T + 1)

As both would've covered a TOTAL of 34 miles, when they meet, we get the following DISTANCE equation: 6T + 4(T + 1) = 34
                                                                                                        6T + 4T + 4 = 34
                                                                                                                10T = 30
<font color = red><font size = 4><b>Time they took to meet, after Amanda starts hiking</font></font></b>, or {{{T = 30/10}}} = <font color = red><font size = 4><b>3 hours</font></font></b></pre>