Question 508371
Richard had to arrive at the airport at exactly 10 am. 
If he is able to drive at an average speed of 60 miles per hour he would arrive early at 9 am. If he drives at an average speed of 40 miles per hour he would arrive late at 11am. 
How fast should he travel to arrive at the airport at 10 am exactly?
:
Let d = the distance
Let s = the speed required to arrive on time
:
Write a time equation for each scenario
{{{d/s}}} - {{{d/60}}} = 1 hr (early)
{{{d/40}}} - {{{d/s}}} = 1 hr (late)
:
Multiply by a common denominator in each to clear the denominator
 60d - ds = 60s; multiplied by 60s
and
 ds - 40d = 40s; multiplied by 40s
Arrange these two equation for elimination
+60d - ds = 60s
-40d + ds = 40s
-------------------adding eliminates ds leaving us with
20d = 100s
Divide both sides by 20
d = 5s
Using the 1st equation replace d with 20s
{{{(5s)/s}}} - {{{(5s)/60}}} = 1 hr
5 - {{{(5s)/60}}} = 1
-{{{(5s)/60}}} = 1 - 5
-{{{(5s)/60}}} = -4
Cancel 5 into 60
-{{{s/12}}} = -4
multiply both sides by -12; 
s = -12*-4
s = +48 mph is the required speed to arrive on time
:
:
Find the distance and check the solution in the 2nd equation
d = 5(48)
d = 240 mi
{{{240/40}}} - {{{240/48}}} = 1 hr 
  6 hrs - 5 hrs = 1 hr