There are 2 trains, one in Los Angeles and the other one in Denver. Train 1 left Los Angeles at 10am and was traveling east at a speed of 100 mph. Train 2 left Denver at 1pm and was traveling west at 80 mph. Which train is closer to Los Angeles when they meet each other?
at 1 pm Train 1 had gone 300 miles.
Now you know that one train is going 5/4 as fast as the other.
see what you can do from here.
To determine which train is closer to Los Angeles when they meet each other, we need to calculate the distance traveled by each train at the time of their meeting.
First, let's calculate the distance traveled by Train 1. The time elapsed from 10 am to the time of meeting is the same for both trains, so we will consider that time as 't'.
Distance traveled by Train 1 = Speed of Train 1 x Time
= 100 mph x t
Now, let's calculate the distance traveled by Train 2. The time elapsed from 1 pm to the time of meeting is 't - 3' hours (since Train 1 started three hours earlier).
Distance traveled by Train 2 = Speed of Train 2 x Time
= 80 mph x (t - 3)
To find when the two trains meet, we will set the distances equal to each other, since they will be the same at the point of intersection:
100t = 80(t - 3)
Simplifying the equation:
100t = 80t - 240
20t = 240
t = 12
So, the trains meet 12 hours after Train 1 departs, which is at 10 am + 12 hours = 10 pm.
Now, substitute t = 12 into the distance formulas:
Distance traveled by Train 1 = 100 mph x 12 = 1200 miles
Distance traveled by Train 2 = 80 mph x (12 - 3) = 720 miles
Therefore, Train 1 is closer to Los Angeles when they meet, as it has traveled a shorter distance (1200 miles) compared to Train 2 (720 miles).