Two runners leave the starting gate, one running 12 mph and the other 10 mph. If they maintain the pace, how long will it take for them to be one-quarter of a mile apart?

1 Answer
May 12, 2018

#1/8\ "hour"#

Explanation:

#"Time" = "Relative Distance"/"Relative Velocity" = "1/4 miles"/"12 mph – 10 mph" = 1/8\ "hour"#

CHECK
Distance travelled by them after #1/8# hour

#"d"_1 = "12 mph" × 1/8\ "mph" = 12/8\ "miles"#

#"d"_2 = "10 mph" × 1/8\ "mph" = 10/8\ "miles"#

Separation

#"Δd" = 12/8\ "miles" - 10/8\ "miles" = ((12 - 10)\ "miles")/8 = 1/4\ "miles"#