A freight train leaves St. Louis traveling at 85 km/hr.
One hour later, a passenger train leaves St. Louis on a parallel track traveling 105 km/hr.
When will the 2nd train overtake the first train?
How far from St. Louis will the passenger train overtake the freight train?
a) Let h=
the time the first train spends traveling. Write the equation you would use to find this time.
__hours after the first train left, the 2nd train overtakes the first train. (Round to one decimal place.)
When the 2nd train catches up, the trains have traveled ___ kilometers.
To find the time the first train spends traveling, we can use the equation:
distance = speed × time
Let's call the time the first train spends traveling "h" hours. The distance traveled by the first train will be 85h km.
Given that the second train leaves one hour later than the first train, the time it takes for the second train to overtake the first train will be h - 1 hours.
To find how far from St. Louis the second train overtakes the first train, we can multiply the speed of the second train (105 km/hr) by the time it takes for the second train to catch up with the first train (h - 1 hours).
Therefore, the equation to find the time the first train spends traveling is:
85h = 105(h - 1)
Now, let's solve for h:
85h = 105h - 105
20h = 105
h = 105/20
h ≈ 5.3 hours
Therefore, it will take approximately 5.3 hours for the second train to overtake the first train.
To find how far from St. Louis the second train overtakes the first train, we substitute the value of h back into the equation for the distance traveled by the second train:
Distance = Speed × Time
Distance = 105 × (5.3 - 1)
Distance = 105 × 4.3
Distance ≈ 451.5 kilometers
Therefore, when the second train catches up, the trains have traveled approximately 451.5 kilometers.
To find the time it takes for the first train to travel, we can use the equation:
distance = speed * time
Let h = the time the first train spends traveling. The distance for the first train can be expressed as distance1 = speed1 * h, where speed1 = 85 km/hr.
The second train leaves one hour later, so its time is h - 1. The distance for the second train can be expressed as distance2 = speed2 * (h - 1), where speed2 = 105 km/hr.
Both trains have traveled the same distance when the second train overtakes the first train, so we can set distance1 = distance2:
85h = 105(h - 1)
Now, we can solve this equation to find the value of h:
85h = 105h - 105
105 - 85 = 105h - 85h
20 = 20h
h = 1
Therefore, it will take the first train 1 hour to travel.
To find the distance from St. Louis when the second train overtakes the first train, we can substitute the value of h into either distance1 or distance2:
distance1 = 85 * 1 = 85 km
Therefore, when the second train overtakes the first train, the trains have traveled 85 kilometers.