solve basic word problems

A bus station runs a shuttle service to and from the airport. A shuttle that left the station traveling at 27 miles per hour is passed by a second shuttle that left 15 minutes later traveling at a rate of 42 miles per hour. How far did the first shuttle travel before it was passed by the second shuttle? If the answer is not an integer, enter it as an exact decimal

A single-engine aircraft leaves a landing strip traveling to Dallas, 67.6 miles away, at an average speed of 220 miles per hour. Twelve minutes later, a private aircraft leaves the Dallas airport traveling at an average speed of 252miles per hour heading towards that same landing strip.
At the moment when the two aircrafts pass each other, how far (in miles) is the single-engine airplane from the landing strip and how long (in minutes) has it been traveling?

Omar skateboarded from the arcade to work at an average speed of 15 miles per hour, and then skateboarded back the same way at an average speed of 11 miles per hour. If the round trip took 1 hour and 30 minutes, how many miles is Omar's one-way trip from the arcade to work?

>>2578859>>257885
90=11x +15x

>>257883
Distance of first shuttle: 27h + 27/4 (extra distance from 15 minutes head start)
Distance of second shuttle: 42h
Since we know the second shuttle catches up
27h + 27/4 = 42h
27/4 = 15h
27/60 = h

Distance of first shuttle: 27h + 27/4
= 27(27/60) + 27/4 Use a calculator to figure out the answer.

>>257884
Distance of first aircraft: 220h + 220(12/60)
Distance of second aircraft: 252h
Since we know they meet up along the 67.6 miles
67.6 = 252h + 220h + 220(12/60)
472h = 67.6 - 220/5
472h = 67.6 - 44
472h = 23.6
h = 23.6/472 This is how long the second plane has been travelling. Add 12 minutes to get how long the first plane was travelling

Distance of first aircraft: 220h + 220(12/60)
= 220(23.6/472) + 44 This is how far the first plane has travelled from the landing strip. As usual, use a calculator.

>>257885
Let t represent the time Omar spent skateboarding to work.
Since we know the distance is the same both ways,
15t = 11(1.5 - t)
15t = 11(1.5) - 11t
26t = 11(1.5)
t = 11(1.5)/26

Since Omar went at a speed of 15 miles per hour to get to work, the distance is:
15*11*1.5/26 Use a calculator. Hope this helps :)