A train leaves the train station at noon and travels at a constant speed of vt =
ID: 1587232 • Letter: A
Question
A train leaves the train station at noon and travels at a constant speed of vt = 50 mi/hr on a straight track. At 2:00 PM, a car leaves the same train station and travels in the same direction at vc = 70 mi/hr on a road next to the train track. 1) How far has the train traveled at 3:00 PM? 2) How far has the car traveled at 3:00 PM? 3) How long after 12:00 noon is the car exactly 210 miles from the station? (Enter your answer as a decimal number of hours - not the number of hours and minutes. 4) How long after 12:00 noon does the car catch up with the train? (Again, enter your answer as a decimal number of hours - not the number of hours and minutes.) 5) How far from the station is the place where the car catches up with the train?
Explanation / Answer
1) t= 3 hours = 3*60 =180 s
distance travelled by train is d = velocity*time = 50*3 = 150 miles
2) distance travelled by car is dc = 70*1 = 70 miles
3) given that d-dc = 210 miles
(50*t)-(70*(t-2)) = 210 miles
20*t = 210-140
t = 70/20 = 3.5hours
4) d = dc
50*t = 70*(t-2)
20*t = 140
t = 7 hours
5) d = 50*7 = 350 miles
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