SOLUTION: A train traveling at the rate of 90 miles per hour (mi/hr) leaved New York City. Two hours later, another train traveling at the rate of 120 mi/hr also leaves New York City on a pa
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Question 1059932: A train traveling at the rate of 90 miles per hour (mi/hr) leaved New York City. Two hours later, another train traveling at the rate of 120 mi/hr also leaves New York City on a parallel track. How long will it take the faster train to catch up to the slower train? Found 3 solutions by stanbon, algebrahouse.com, josgarithmetic:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A train traveling at the rate of 90 miles per hour (mi/hr) left New York City. Two hours later, another train traveling at the rate of 120 mi/hr also leaves New York City on a parallel track. How long will it take the faster train to catch up to the slower train?
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Slower train DATA:
rate = 90 mph ; time = x hrs ; distance = 90x miles
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Faster train DATA:
rate = 120 mph ; time = x-2 ; distance = 120x - 240 miles
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Equation:
dist = dist
90x = 120x - 240
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-30x = -240
x = 8
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Ans: x-2 = 6 hrs
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Cheers,
Stan H.
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One Train:
rate = 90
time = t
d = 90t {distance = rate x time}
Other Train
rate = 120
time = t - 2 {left 2 hours later}
d = 120(t - 2) {distance = rate x time}
When the faster train catches up with the slower train, their distances will be equal.
90t = 120(t - 2) {set distances equal to each other}
90t = 120t - 240 {used distributive property}
-30t = -240 {subtracted 120t from each side}
t = 8 {divided each side by -30}
t - 2 corresponds to the time of the faster train
= 8 - 2 {substituted 8, in for t, into (t - 2)
= 6 {subtracted}
It will take the faster train 6 hours to catch up with the slower train.
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