Question 1164836
Sean drove at a uniform speed of 90km/h. He started driving at 5:30 am and
reached his destination at 1.30 pm. Mary started driving at the same time as
Sean and reaches the same destination in 6 hrs. How far was Sean from his
destination when he was 150 km apart from Mary?
<pre>Sean traveled a total of 8 hrs (5:30 am - 1:30 pm), and at 90 km/h, destination-distance was: 8(90), or 720 km
With  Mary taking 6 hours to complete trip, her speed was:{{{matrix(1,4, 720/6, "=", 120, "km/h")}}}
You must realize that Mary's rate was faster than Sean's (120 km/h to 90 km/h), which means that she was ahead of him after they left the same location
at the same time and were heading to the same destination

Let the distance Mary was, from the destination be x
Then Sean was 150 + x from destination when Mary was 150 km in front of him
When Sean was 150 km from Mary, he'd traveled 570 - x from the starting point, in {{{(570 - x)/90}}} hours
When Mary was 150 km IN FRONT of Sean, she'd traveled 570 - x + 150 from the starting point, in {{{matrix(1,5, (570 - x + 150)/120, or, (720 - x)/120, "=", 6 - x/120)}}} hours
With both leaving the same location at the sane time, they reached their respective distances at the sane time.
We then get the following TIME equation: {{{matrix(1,3, (570 - x)/90, "=", 6 - x/120)}}}
4(570 - x) = 2,160  - 3x ------ Multiplying by LCD, 360
2,280 - 4x = 2,160  - 3x
 - x = - 120 ====> {{{matrix(1,5, x, "=", (- 120)/(- 1), "=", 120)}}}
Therefore, when Mary was 150 km in front of Sean, Sean was 150 + 120, or {{{highlight_green(matrix(1,2, 270, km))}}} from the destination.