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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Trains A and B are 190 miles apart.
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05 Apr 2019, 06:46
05 Apr 2019, 06:46
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Question Stats:
90% (01:30) correct
9% (00:37) wrong based on 53 sessions
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Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15 miles per hour directly toward train B. Train B travels at 10 miles per hour directly toward train A. When the trains meet, how many miles has train A traveled?
Show: ::
120
Re: Trains A and B are 190 miles apart.
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05 Apr 2019, 10:19
05 Apr 2019, 10:19
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GreenlightTestPrep wrote:
Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15 miles per hour directly toward train B. Train B travels at 10 miles per hour directly toward train A. When the trains meet, how many miles has train A traveled?
Show: ::
120
Here,
Since the train A started 1 hour before train B, hence in 1 hr, Train A travelled = 15 miles,
Now Train A and Train B are 190 - 15 = 175 miles apart.
The time required to meet = \(\frac{175}{{15+10}}\) = \(7\) hr
Hence the Train A travelled = \(15 + ( 15 * 7)\) = 120 miles
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Trains A and B are 190 miles apart.
[#permalink]
06 Apr 2019, 07:19
06 Apr 2019, 07:19
1
GreenlightTestPrep wrote:
Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15 miles per hour directly toward train B. Train B travels at 10 miles per hour directly toward train A. When the trains meet, how many miles has train A traveled?
Show: ::
120
The great thing about these "multiple traveler" questions is that they can be solved in more than one way.
All we need to do is start with a word equation.
Since Train A travels for 1 hour longer than Train B, we can write:
Train A's travel time = (Train B's travel time) + 1
Let d = the distance Train A traveled
This means that 190 - d = the distance Train B traveled
Now let's transform our word equation into an algebraic equation.
Train A's travel time = (Train B's travel time) + 1
Time = distance/speed
We get: d/15 = (190 - d)/10 + 1
Multiply both sides by 30 to get: 2d = 570 - 3d + 30
Simplify: 2d = 600 - 3d
Add 3d to both sides: 5d = 600
Solve: d = 120
Answer: 120
