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Speed/Distance

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Speed/Distance

by vaibhav101 » Wed Jun 06, 2018 9:03 am

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Train A leaves New York for Boston at 3 pm and travels at a constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If train B left Boston at 3:50 pm and if the combined travel time of the 2 trains is 2 hours, what time did Train B arrive in New York ?

1) Train B arrived in New York before Train A arrived in Boston
2) the distance between New York and Boston is greater than 140 miles
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Source: — Data Sufficiency |
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by deloitte247 » Thu Jul 26, 2018 2:41 pm

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Question: What time did train B arrived in New York.
Let x be the train distance between cities
Let y be the rate of train B
An hour later [4 : 00pm] train A passes train B before they passed each other train A traveled 1 hour and B traveled $$\frac{1}{6}hours\ \left[3:50\ -\ 4:00pm\right]$$
Combined travelling time for the two times is 2hours
$$\frac{x}{100}\left[time\ to\ cover\ all\ dis\tan ce\ from\ train\ A\right]$$
$$\frac{x}{y}\left[time\ to\ cover\ all\ dis\tan ce\ from\ train\ B\right]$$
$$\frac{x}{100}+\frac{x}{y}=\ 2$$
Before passing each other, train A traveled at 100 miles [per hour] distance that train B will cover
$$100miles+current\ speed\cdot\left(\frac{1}{6}\right)\ miles\ \cdot\left[\frac{1}{6}\ \frac{\left(hour\ city\ miles\right)}{hour}\right]$$
distance for A cover after they pass each
$$other\ =\ y\ \cdot\frac{1}{6\ }miles$$
$$=\ 100\ +\ \frac{y}{6}\ x$$
$$Therefore,\ \frac{x}{100}\ +\ \frac{x}{y\ }and\ 100\ +\frac{y}{6}\ =\ x$$
Solving for x and y
x = 150 and y = 300
$$x\ =\ \frac{800}{6}=\ 133.3\ and\ y\ =\ 200$$

Statement 1; Train B arrived in New York before Train A arrived in Boston.
If y = 200 A arrives at 4: 20pm and B = 4: 30pm
If y = 300 A arrives at 4. 30pm and B = 4: 40pm
Hence statement 1 is sufficient

Statement 2 = The distance between New York and Boston is greater than 140miles.
x>140
x= 150 and
y = 300
Time of arrival for Train B = 4: 20pm
Hence, statement 2 is also sufficient
Therefore, Option C is the correct answer.
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