Question

Two trains started moving at the same time, train A from Boston to New York, and train B from New York to Boston. The distance between the train stations in New York and Boston is 240 miles. The average speed of train A is 60 mph, which is 3/4 of the average speed of train B.
How soon will the trains meet?

Answer 1

Answer:

• After 1.7 hours

Explanation:

1. Calculate the average speed of train B

• 60mph = 3/4 (s) ⇒ s = 60 (4/3) mph = 80 mph

2. Build a table

When the two trains meet:

Train     Average speed     Distance       time (distance/average speed)

                 mph                            

A                 60                             x                        x/60

B                 80                        240 - x                (240 - x) / 80

3. Write the equation

The time, when the two trains meet, is the same for both trains:

                  $\dfrac{x}{60}=\dfrac{240-x}{80}\\ \\ \\ 80x=14,400-60x\\ \\ 80x+60x=14,400\\ \\ 140x=14,400\\ \\ x=14,400/140\\ \\ x=102.85miles$

4. Calculate the time:

• x/60 = 102.86 / 60 = 1.7 hours

The two trains will meet after 1.7 hours