BTGModeratorVI wrote: ↑

Wed Apr 22, 2020 11:07 am

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

Answer: E
Source: Veritas Prep

Miles traveled by Train A in 1 hour = 15*1 = 15 miles;

Miles to covered by both trains = 190 – 15 = 175 miles

Since the trains are moving towards each other, miles covered by Train A and Tarin B would be in the ratio of 10 : 15 => 3 : 2

Miles covered by Train A = 175*[3/(2 + 3)] = 105 miles

Total miles covered by train A = 15 + 105 = 120 miles

The correct answer: E

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Wed Apr 22, 2020 11:07 am

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

Answer: E
Source: Veritas Prep

Solution:

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 miles 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 thus 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.

Alternate Solution:

After one hour, train A has traveled 15 miles, so the distance between the two trains is 190 - 15 = 175 miles.

When both trains are moving, the distance between them is decreasing 15 + 10 = 25 miles each hour; therefore, the two trains will meet in 175/25 = 7 hours. Together with the first hour, train A has traveled 1 + 7 = 8 hours in total, and thus when the two trains met, train A has traveled 8 * 15 = 120 miles.

Answer: E