# A train made a trip to New York and back. On the trip there it traveled 22 mph and on the return trip it went 10 mph. How long did the trip there take if the return trip took 11 hours?

Dec 5, 2015

$16$ hours for the round trip

#### Explanation:

Part 1: determining the distance traveled
We are told the return trip took 11 hours at a speed of 10 mph.
$\text{distance" = 11 cancel( " hours") xx (10 " miles")/(cancel("hour")) = 110 " miles}$

Part 2: determine time to travel to New York
We are told that the train traveled at a speed of 22 mph on its way to New York.
Combining this with our knowledge that the distance is 110 miles:

$\text{time to travel to New York}$
color(white)("XXX") = 110 cancel(" miles")xx ("hours")/(22 cancel(" hours"))

color(white)("XXX") = 5 " hours".

Part 3: determine the total time

$\text{total time}$
color(white)("XXX")=" time to New York" + " return time"

color(white)("XXX")= 5 " hours" + 11 " hours"

color(white)("XXX") = 16 " hours"