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At 1:00 PM, Train X departed from Station A on the road to Station B.
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06 Aug 2021, 07:51
06 Aug 2021, 07:51
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64% (03:21) correct
35% (02:27) wrong based on 17 sessions
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At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y ’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?
A. \(\frac{1}{2}+\frac{p-\frac{s}{2}}{r+s}
\)
B. \(\frac{p-\frac{s}{2}}{r+s}\)
C. \(\frac{1}{2}+\frac{p-\frac{s}{2}}{r}\)
D. \(\frac{p-\frac{s}{2}}{r+s}\)
E. \(\frac{1}{2}+\frac{p-\frac{r}{2}}{r+s}\)
A. \(\frac{1}{2}+\frac{p-\frac{s}{2}}{r+s}
\)
B. \(\frac{p-\frac{s}{2}}{r+s}\)
C. \(\frac{1}{2}+\frac{p-\frac{s}{2}}{r}\)
D. \(\frac{p-\frac{s}{2}}{r+s}\)
E. \(\frac{1}{2}+\frac{p-\frac{r}{2}}{r+s}\)
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At 1:00 PM, Train X departed from Station A on the road to Station B.
[#permalink]
07 Aug 2021, 08:12
07 Aug 2021, 08:12
1
Carcass wrote:
At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:30 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y ’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?
A. \(\frac{1}{2}+\frac{p-\frac{s}{2}}{r+s}\)
B. \(\frac{p-\frac{s}{2}}{r+s}\)
C. \(\frac{1}{2}+\frac{p-\frac{s}{2}}{r}\)
D. \(\frac{p-\frac{s}{2}}{r+s}\)
E. \(\frac{1}{2}+\frac{p-\frac{r}{2}}{r+s}\)
A. \(\frac{1}{2}+\frac{p-\frac{s}{2}}{r+s}\)
B. \(\frac{p-\frac{s}{2}}{r+s}\)
C. \(\frac{1}{2}+\frac{p-\frac{s}{2}}{r}\)
D. \(\frac{p-\frac{s}{2}}{r+s}\)
E. \(\frac{1}{2}+\frac{p-\frac{r}{2}}{r+s}\)
Since the trains are moving in opposite direction, the relative speed would be the sum of their individual speeds
i.e. \(v_{rel} = (r + s)\) mph
Train departed at 1:00 PM and travelled \(\frac{r}{2}\) miles till 1:30 PM
So, the distance left between X and Y = \((p - \frac{r}{2})\)
Time required to cross each other = \(\frac{p-\frac{r}{2}}{r+s}\)
Don't forget to add \(\frac{1}{2}\) into it as the question reads - how many hours after 1:00 PM, ....
i.e. \(\frac{1}{2}+\frac{p-\frac{r}{2}}{r+s}\)
Hence, option E
gmatclubot
At 1:00 PM, Train X departed from Station A on the road to Station B. [#permalink]
07 Aug 2021, 08:12
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