## anonymous one year ago Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 16 miles per hour slower than the eastbound train. If the two trains are 320 miles apart after 2 hours, what is the rate of the westbound train? Do not do any rounding.

1. mathstudent55

|dw:1444608714555:dw|

2. mathstudent55

|dw:1444608927631:dw|

3. mathstudent55

$$speed = \dfrac{distance}{time}$$ $$distance = speed \times time$$ Distance traveled by the eastbound train: $$d = st$$ $$d = 2v$$ Distance traveled by the eastbound train: $$d = st$$ $$320 - d = 2(v - 16)$$ Sum of the distances = 320 miles: $$~~~~~~~~~~~d = 2v$$ $$320 - d = 2(v - 16)$$ Add the two equations above: $$d + 320 - d = 2v + 2(v - 16)$$ $$320 =2v + 2v - 32$$ $$320 = 4v - 32$$ $$352 = 4v$$ $$v = 88$$ The eastbound train travels at 88 mph. The westbound train travels at 88 mph - 16 mph = 72 mph Check: In 2 hours, the eastbound train travels 2 * 88 miles = 176 miles In 2 hours, the westbound train travels 2 * 72 miles = 144 miles Since 176 miles + 144 miles = 320 miles, our answer is correct.

4. mathstudent55

Please note that the answer is 72 mph, since the question asks for the speed of the westbound train.

5. anonymous

Thank you Thank you so much. Oh my god I love you.

6. mathstudent55

You're welcome.