Dan took a train to his vacation spot. His train travels 75 miles each hour before making a stop. He left the station at 10:00. Phil is taking a vacation to the same spot, except his train travels 60 miles each hour before making a stop. Phil’s train left the station at 8:00. What time will they be in the same place?

Accepted Solution

Answer:6pmStep-by-step explanation:Assumption: Both Dan and Phil both depart from the same station and arrive at the same station. (i.e they both travel the same distance)Dan's travel speed is 75mph and Phil's travel speed is 60mphLet Dan's travel time be [tex]t_{Dan}[/tex] and Phil's travel time be [tex]t_{Phil}[/tex] Use Formula Distance travelled = speed x time, henceDan's Distance Travelled =75 [tex]t_{Dan}[/tex]Phil's Distance Travelled =60 [tex]t_{Phil}[/tex]Because they travel the same distance, we can equate the 275 [tex]t_{Dan}[/tex] = 60 [tex]t_{Phil}[/tex]or [tex]t_{Dan}[/tex] = (60/75) [tex]t_{Phil}[/tex][tex]t_{Dan}[/tex] = 0.8 [tex]t_{Phil}[/tex]  -------> eq 1We also know that Dan left at 10:00 and Phil left at 8:00. If they end up being at the same place, this means that Phil's journey will be 2 hours longer than Dan, or[tex]t_{Phil}[/tex] = [tex]t_{Dan}[/tex] + 2------> eq2we can solve the system of 2 equations to get[tex]t_{Phil}[/tex] = 10 hrs[tex]t_{Dan}[/tex] = 8 hrsIf Phil left at 8:00 am, he will be in the same place as Dan at 8:00 + 10 hrs = 6 pm.Double Check:If Dan left at 10:00, he will be in the same place as Phill at 10:00 + 8 hrs = 6 pm.