At noon a train leaves Della for Midtown, 800 km South. At 2 P.M., A train on a parallel track leaves Midtown for Della. If each track travels at 75km/hr, at what time will they pass each other?

Answer 1

t is the time of the northbound train...

then the southbound train has traveled for t+2 hours, or 2 hours more

75t + 75(t+2) = 800

75t + 75t + 150 = 800

150t = 650

t = 650/150 = 65/15 = 13/3 = 4 and 1/3 = 4 hours and 20 minutes

the northbound train travels for 4 hours and 20 minutes, or 13/3 hours,

which, at 75 km per hour, is 325 km

the southbound train travels for 6 and 1/3 hours = 6 hours and 20 minutes

which, at 75 km per hour is 475 km

these distances in fact total 800 km.

Therefore, they will meet at 6:20 pm

the following table verifies this results that

the trains will be at the same spot at 6:20 pm

Time location of southbound train location of northbound train

12 pm leaves Della Station Midtown Station

1 pm 75 km south of Della Midtown Station

725 km north of Midtown

2 pm 150 km south of Della leaves Midtown Station

650 km north of Midtown

3 pm 225 km south of Della 75 km north of midtown

575 km north of Midtown 725 km south of Della

4 pm 300 km south of Della 150 km north of midtown

500 km north of Midtown 650 km south of Della

5 pm 375 km south of Della 225 km north of midtown

425 km north of midtown 575 km south of Della

6 pm 450 km south of Della 300 km north of midtown

350 km north of midtown 500 km south of della

6:20 475 km south of Della 325 km north of midtown

325 km north of midtown 475 km south of Della