Trains A and B are 190 miles apart. Train A leaves one hour

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alanforde800Maximus: Master | Next Rank: 500 Posts; Posts: 187; Joined: Tue Sep 13, 2016 12:46 am

by alanforde800Maximus » Mon Oct 17, 2016 9:48 pm

Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?

a) 70
b) 85
c) 95
d) 105
e) 120

Please assist with above problem.

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Source: Beat The GMAT — Problem Solving | Mon Oct 17, 2016 9:48 pm

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by GMATGuruNY » Mon Oct 17, 2016 11:28 pm

alanforde800Maximus wrote:Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?

a) 70
b) 85
c) 95
d) 105
e) 120

In the first hour, the distance traveled by A alone = rt = 15*1 = 15 miles.

Remaining distance between A and B = 190-15 = 175 miles.
Since A and B now travel TOWARD EACH OTHER, they WORK TOGETHER to cover the remaining 175 miles between them.
Combined rate for A and B working together = (A's rate) + (B's rate) = 15+10 = 25 miles per hour.
Of every 25 miles traveled when A and B work together, A travels 15 miles.
Implication:
A will travel 15/25 of the remaining 175 miles:
(15/25)(175) = (3/5)(175) = 105.

Total distance traveled by A = 15+105 = 120 miles.

The correct answer is E.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8134; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Oct 20, 2016 5:23 am

alanforde800Maximus wrote:Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?

a) 70
b) 85
c) 95
d) 105
e) 120

Please assist with above problem.

We are given that trains A and B are traveling toward each other, so we have a "converging rate problem" in which we can use the formula:

Distance traveled by train A + Distance traveled by train B = total distance

Since the two trains started 190 apart, the total distance is 190, so we have:

Distance traveled by train A + Distance traveled by train B = 190

We are given that train A travels at a rate of 15 mph and leaves one hour before train B. We are also given that train B travels at a rate of 10 mph.

We can let the time of train B = t and, since train A left one hour earlier and will have traveled for one more hour than train B, at the time they meet, the time of train A = t + 1.

Since rate x time = distance, we can calculate the distance, in terms of t, of both trains A and B.

Distance of train A = 15(t + 1) = 15t + 15

Distance of train B = 10t

Now we can substitute these values into our total distance formula and determine t.

15t + 15 + 10t = 190

25t = 175

t = 7

Thus, when the trains meet, train A has traveled (15 x 7) + 15 = 120 miles.

Answer: E

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Oct 20, 2016 7:39 am

alanforde800Maximus wrote:Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?

a) 70
b) 85
c) 95
d) 105
e) 120

Please assist with above problem.

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.
In Scott's solution, he starts with the following word equation: Distance traveled by train A + Distance traveled by train B = total distance

Let's try a different 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: E

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fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

by fiza gupta » Thu Oct 20, 2016 6:16 pm

A starts one hour early: distance travelled in that one hour : 15
distance left between train A and Train B(when B will start) : 190-15 = 175

when train move in opposite direction : we add their speed : 15+10 = 25
let t be the time when they both meet and distance will be 175
t = 175/25 = 7

Distance travelled by A : 15(in one hour) + 15*7(in next 7 hours,till the time they meet)
= 15 + 105 = 120
SO E

Fiza Gupta

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Oct 28, 2016 12:13 am

Let's make t = Train A's time, since we want to find Train A's distance.

Train A's D + Train B's D = 190

Train A's D = 15*t
Train B's D = 10*(t - 1)

so

15*t + 10*(t - 1) = 190

and t = 8.

Train A's D = 15*t = 15*8 = 120

and we're done!

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rohit56: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Sat Dec 15, 2018 12:06 am

by rohit56 » Sat Dec 15, 2018 3:33 am

Train A would travel 15 miles in 1 hour before Train B starts moving.
So, the distance left between the train = 190 - 15 = 175 miles.
Now, train B has also started moving at 10mph towards train A.
Since, both of them are traveling towards each other, we can add their speed to find the time taken to meet.
Time taken to meet = 175/25 = 7 hr.
Distance traveled by train A = 7 x 15 + 15 = 120 miles.
Hence E.

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