Evaluate distance traveled by train:

A plane flying at 525 miles per hour completes a trip in 2 hours less than another plane flying at 350 miles per hour.  What is the distance travelled?

Solution:

Step 1. Let x = Distance Traveled (in miles)

Step 2. Then, using Equation 14,

x/525 = Time Taken by Faster Plane (in hours)

x/350 = Time Taken by slower Plane (in hours)

Step 3. Time Taken by Faster Plane = Time Taken by Slower Plane - 2 hours

x/ 525 hours = x/350 hours -2 hours

x/525 = x/ 350 -700/350

x/525 = x-700/ 350

(350)(525) (x/525) = (x - 700/ 350) (350)(525)

350x = 525. (x - 700)

350x = 525x - 367,500

350x - 525x = -367,500

-175x = -367,5000

-175x /-175 = -367,500/-175

x = 2100 miles

Solving for the other unknowns:

x/525 = Time Taken by faster plane (in hours)

x/525 = 2100/525

x/525 = 4 hours

x/350 = time Taken by slower Plane (in hours)

x/350  = 2100/350

x/350 = 6 hours

Answers:       

Distance Travelled = 2100 miles

Time Taken by Faster Plane = 4 hours

Time Taken by Slower Plane = 6 hours

Step 5. The faster plane takes 2 hours less to complete the trip than the slower plane.

6 hours - 2 hours = 4 hours

Thus, the answer checks.