Problem Solving

AAPL wrote:Train X leaves New York at 1 A.M. and travels east at a speed of x miles per hour. If train Z leaves New York at 2 A.M. and travels east, at what rate of speed will train Z have to travel in order to catch train X at exactly 5:30 A.M.?

A. 5x/6
B. 9x/8
C. 6x/5
D. 9x/7
E. 3x/2

Train X leaves at 1 A.M. and Train Z leaves New York at 2 A.M.
When they meet at 5:30 A.M., Train X's travel time will be 4.5 hours, and Train Z's travel time will be 3.5 hours
Also recognize that, when the trains meet, they both will have traveled the same distance.

We know that Train X travels at x mph, and we want to find Train Z's speed.
So, let z = Train Z's speed (in mph)

Now let's create an equation we can work with!

Let's start with a word equation:
Distance traveled by Train X = Distance traveled by Train Z
distance = (time)(speed)

So, we get: (4.5 hours)(x mph) = (3.5 hours)(y mph)
Simplify: 4.5x = 3.5y
Solve for y to get: = 4.5x/3.5
Check answer choices....not there.
So, take 4.5x/3.5, and multiply top and bottom by 2 to get the EQUIVALENT fraction: 9x/7
Check answer choices....answer: D

Cheers,
Brent

Hi All,

We're told that Train X leaves New York at 1 A.M. and travels east at a speed of X miles per hour and train Z leaves New York at 2 A.M. and also travels east on the same route. We're asked at what rate of speed train Z will have to travel in order to catch train X at exactly 5:30 A.M. This question can be solved in a couple of different ways, including by TESTing VALUES.

When TESTing VALUES, you normally won't use the number 1. Here though, the five answer choices would all be different if X=1, so we can use that value here.

Train X travels 1 mile/hour. From 1:00 am to 5:30am, that train would travel 4.5 miles

Since train Z started at 2:00 am, it only travels for 3.5 hours, so we can use the Distance Formula to determine how fast it would need to go to travel that same 4.5 mile distance:
Distance = (Rate)(Time)
4.5 miles = (Rate)(3.5 hours)
(4.5)/(3.5) = Rate
9/7 = Rate
Thus, when X=1, train Z would have to travel 9/7 miles/hour. There's only one answer that matches...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

AAPL wrote:Train X leaves New York at 1 A.M. and travels east at a speed of x miles per hour. If train Z leaves New York at 2 A.M. and travels east, at what rate of speed will train Z have to travel in order to catch train X at exactly 5:30 A.M.?

A. 5x/6
B. 9x/8
C. 6x/5
D. 9x/7
E. 3x/2

Since we have a catch-up problem, we can use the formula: Distance 1 = Distance 2.

The rate of train X is x, and the time is 4.5 hours. We can let the rate of train Z = r, and the time is 3.5 hours. Thus:

4.5x = 3.5r

45x = 35r

9x = 7r

9x/7 = r

Answer: D